The strategies I go over here will be primarily from the perspective of someone playing in Hero Mode. You can still use these strategies when playing in normal mode, it's just that it's not as essential since it is a lot easier to survive since you may gain hearts still and you don't take extra damage.
Before you consider trying to take on this challenge, make sure the items you can take with you are upgraded to their strongest versions. You want to be able to finish this as quickly as possible and having the strongest weapons will help with that. So you should have the complete Master Sword with you, (at a minimum) the Goddess Shield (the Sacred Shield upgraded twice) and the Sacred Bow (the Bow upgraded twice). It will also help if you come in with the maximum bombs and arrows, that way you won't be searching for them when you need it.
Although you can't use items during the challenge, you can use them just before. So certain items that give buffs over time can still have their effect as you enter the challenge. For maximum effectiveness, you should bring with you the Guardian Potion+ (the Guardian Potion infused once) with the Potion Medal. Just before you start the challenge, drink the Guardian Potion+ that way you'll have nine minutes of invulnerability. This will give you enough time to save your hearts for the most difficult bosses in the beginning of the challenge. Optionally, you can also take a Stamina Potion+ (the Stamina Potion infused once) too but you really won't need it.
The first boss you choose should be the most difficult boss available that way you make good use of the Guardian Potion+ if you're expecting to take a lot of hits:
When playing the normal mode, I personally found that Koloktos was probably the most difficult of the bosses to not get hurt in. Some of its attacks are just hard to anticipate and prepare for since it has a lot of range and you have to be close for them to come out. Unless you don't mind a long battle waiting for the right attacks to come out, I would recommend doing this one first. Otherwise, it's your choice here. Keep in mind that if you come in using the Guardian Potion+, you don't want to waste too much time.
When playing in Hero Mode, I would strongly suggest you do the Horde Battle first (no exceptions). This is probably the most time consuming battles you'll have to go through and so many ways to get hit. They aren't the hardest enemies in the game but there's so many of them and it is easy to get surrounded.
Your primary concern for this challenge above all else is to survive taking as little damage as possible. This might not be too much of a problem when playing in normal mode since you can still find hearts in certain places but it is absolutely essential when you're playing in Hero Mode.
Your shield is your lifeline here, use it. If you're not planning on attacking an enemy, you generally should have your shield out at all times by shaking the Nunchuk. That way you can't get caught off guard and take a hit when you're not paying attention. If you see the attack coming, perform a Shield Bash just before it connects. Your shield won't take damage and it will usually leave the enemy stunned for a second so you can counter.
If your Sacred Shield is getting low on durability, stay away from the enemies and their attacks until your shield fully repairs itself. The last thing you want to have happen is to have your shield be destroyed. Of course if you already have the Hylian Shield, you won't have to worry about this.
For the first part of the battle, he will hold out one hand to try to grab your sword. If you swing your sword right into his hand, he will grab it. To get him to release it, just flick the Wiimote up. Hitting him can be pretty easy. Just hold out your sword in a direction (e.g., to the right, the left, upper-right, etc.) so he will point his hand in that direction. When he does, flick the Wiimote in that direction again so your sword swing will come from the opposite direction. Repeat until the next part of the battle.
At this point, he'll pull out a sword to finally fight now. He has a couple of different attacks here. He will summon darts and shoot them at you. These are easily avoided but could also be knocked back at him. They don't seem to affect him though. He will also teleport around the room every once in a while, some times right next to you. When he does this, be sure to welcome him with a Spin Attack. This will stun him so you can follow up with more hits. He will also charge in at you and swing with his sword. You can pull a Spin Attack here to hit him when he's close enough. The only catch is that the spin has to be right into him. If he charges in at you to your left, you need to perform a Spin Attack spinning to the right. Otherwise, you can Shield Bash at the right time and counter. Repeat until he's dead.
You'll need to get your bombs ready for this battle. When Scaldera is glowing orange with lava, he is invulnerable to your attacks will try to attack you. You need to wait for him to stop glowing. Just run up the ramp until he stops. When he does, turn around and throw a bomb at him. It will knock him back down the ramp, follow him. When he recovers, he will breathe in to blow some fireballs at you. As he does this, throw a bomb at him so he will eat it. This will stun him allowing you to attack his eye. Repeat this until he is dead.
At some point after you have hit him enough times, he will run up the ramp high off the ground. When he does this, just let him run above you up the ramp. He can't hurt you. He will roll down the hill once he reaches the top but you should be able to easily dodge him. When he reaches the bottom, he will breathe in for the fireballs, you know what to do then.
There's not much strategy in fighting this guy, just wait until he exposes the blue eyes in his claws and attack it in the right direction. If the claw eyes turn red, either dodge back or Shield Bash and counter. Same thing if he's about to attack with the tail.
The next phase in the battle, he'll burrow underground. Just pull out the Gust Bellows and blow away the sand until he's exposed and jumps out. When he's out, stab him in the eye. Just be careful when me tries to move away from you, he will almost always do a charge attack or use his tail on you. You can dodge this or Shield Bash and counter. Do this until he's dead.
This battle should be relatively easy. The goal is to jam the spike in his head three times to defeat him. There's two ways to do this. The safest way would be to jump up on top of its head using the higher ledges and hit it down from there. Otherwise you could cut its toes off from both its feet to knock it down. With it down, you could run up to the head and drive the spike up into its head. Just be careful that if you cut any of its toes off, it will start to stomp sending shockwaves that could hurt you. If you manage to cut off all the toes on a foot, it will not do this. After the first time you drive the spike in, it will always send shockwaves at its feet so it would be safer to finish him off by jumping on its head.
Make sure your Whip is equipped. You'll want to draw his attacks so he gets his arms stuck in the ground. He'll only do these attacks if you are close enough to him or after a certain amount of time passes. If you're too far too often, he will throw his axes at you. If too close, he will swipe at you with his axes. When the arms are stuck, use your whip on the stuck arms to break them apart. Do this until all arms are destroyed giving you access to its crystal heart.
Damage the heart enough times will bring phase two of the battle. This time its not stationary and stuck in the middle of the room, it will pull itself out exposing its legs and can move around. This is the more dangerous phase since it has more attacks and is mobile. It will even summon a couple of Cursed Bokoblins to get in your way. They are mostly harmless but kill them off when they get too close.
Again, the goal is to get its arms stuck in the ground so you can pull them apart. It will swing with its left or right set of arms at you at a time or even both. When it's swinging down with one set, dodge back and pull its arms apart. It will drop the swords to the ground where you can pick one up and use as a weapon. After picking one up, wait until it attacks before moving in, you are much more slower this way and can't really block. Move close enough so it is in range of your sword swings and do a horizontal swing at its legs. Doing so will chop its legs off leaving it helpless. You can then wail away at the body to break open the shell and the crystal heart. Repeat the process until it is defeated.
The first thing you want to do is pull out your sword and charge for a Skyward Strike. Tentacles will soon bust out from the deck and these are your targets. Lop off four of them using your Skyward Strikes and Tentalus will come up out of the water to fight you. Just don't do vertical Skyward Strikes as it will not cut them off. Always keep moving so they can't get a hold of you.
When he comes out of the water, get your Sacred Bow ready. You'll need to shoot him in the eye to be able to stun him. To be as quick as possible, use the C button and shake the Nunchuk to pull back your bow then release C to fire. You can shoot arrows off rapidly this way. Try to hit the eye when it is first opened. When you hit him, rush up to him so you can get close and personal with his eye. Just keep doing vertical Spin Attacks as much as you can until he moves away (it will be short enough that you won't tire yourself). If his tentacle hair gets in the way, charge up a Skyward Strike to cut them out of the way. Repeat until the next phase in the battle.
You'll know you're switching over to the next phase of the battle when he hits the deck and barrels start rolling toward you. Run toward the box that dropped down and climb up. Make sure you avoid the barrels.
This phase is mostly the same as the first phase, except this time, his tentacle hair will sprout mouths and start attacking you. Until he's stunned, you need to fight off the tentacle mouths. Just keep swinging your sword horizontally until they stop attacking. Quickly pull out your bow and hit the eye. Like before, rush up to him and hack at his eye. Repeat until he's dead.
This battle will start off pretty much the same as your last encounter with him except this time he will have darts with him to slow you down. You can negate his use of the darts if you charge for a Skyward Strike. Just charge then swing away in the right direction.
This time around, he will pull out two swords and have three times as many darts than he did before. Use pretty much the same strategies here again. When you're close enough to him, he will hold out his swords to block your attacks from certain directions. Just swing in the direction he's not blocking and you can easily hit him multiple times. Some times he will jump up into the air and try to land on you with a downward stab. When he does this, just dodge back and counter when he hits the ground. He will also summon darts surrounding you or in some configuration. Just do an attack that could hit them all at once. If they form a circle around you parallel to the ground, just to a horizontal Spin Attack. Just keep hitting him until he's defeated.
Another fight with The Imprisoned but this time he has arms. I would advise against attacking it's toes this time, the shockwaves it produces when it steps are too frequent to avoid and is easy to get hurt this time. This time, I would suggest jumping onto its head always and drive the spike in from there.
At some point he will try to climb up the walls. You have two options, the easiest would be to switch to Groose and shoot at its hands to knock it down. Otherwise you could go to town on its fingers to knock it down. Once knocked down, just repeat the process above until he's defeated.
In this battle, things get a little complicated. This time around, he grew a tail and can fly later on. Again, I still find it safest to go straight for his head however he will always shake you off. Before you go on to jump onto his head, switch to Groose to hurl a bomb at him. That should stun him long enough for you to be able to jump on his head to drive the spike down.
Doing this, the imprisoned will start to fly. Not a problem though, fortunately Groose will have a bomb ready. Shoot him down. It will knock him into the ground in the center. Get down there and knock the spike into his head.
He will start to fly again but Groose's supply of bombs will be blocked making it unusable. fortunately you still have a perfectly working catapult. Climb up to the top and ride that catapult by shooting yourself onto the imprisoned's head. Once you get there, drive the spike in his head one more time to finish him off.
I consider this battle mostly just a race than a real battle. Most of the enemies you see here will be Bokoblins (and other variations) and can be killed in a single swing of the sword. You don't want to waste too much time fighting off the endless streams of them, you want to make it to the end as fast as possible.
Until you are stopped by a wall and forced to fight, you should be sprinting your way down the kill dodging the enemies that get in your way (remember, you can't have your shield out and sprint at the same time). Try to pick up Stamina Fruits on your way down to minimize the time you have to walk and recover.
When the time comes to fight, you should take care of the horde first. Don't even go near the "specialist" enemies yet until you've dispatched the weaker ones. I find it easy to let them bunch up, run up to the group and do a Spin Attack and step away. Let them bunch up again and repeat. Once you've taken care of the "dumb" Bokoblins, you can go after specialists. Just use your instincts here, there's nothing special about these enemies than what you've already encountered. There is a blue Bokoblin that takes an unusual amount of damage but that's about it.
There will be five phases to this battle each corresponding to when you are forced to stop and fight. The first phase will spawn a bunch of the smarter Bokoblins (the ones that can block your attacks). The second phase you will have to fight three Wooden Shield Moblins. The third phase, you will have to fight off the a Bokoblin. The fourth phase, you will have to fight off two Stalfos. The fifth and final stage, you'll just have to fight off an army of (dumb) Bokoblins at the end.
This battle is about patience. Just about all the attacks he has are counters or must be countered. You're not going to win this battle by blindly flailing around your sword.
The first phase of the battle should be simple. The goal is to knock him down off the platforms so you can perform a Finishing Move on his weak point, the diamond in his chest. In order to do that, just wail away at him until you knock him over the edge. Every once in a while, he will attack you. He will always make an audible noise and change stances before he does so. When you see him do this, dodge back or pull out your shield. After he swings, just continue swinging away.
After you knock him down the first time and he gets close to the edge, he will start to hold out purple flames from his hands. If you hit them, he will counter so you need to not hit them. Take your time here and slow down, there's no rush but don't take too long. Hitting him three times will move on to the second phase of the battle.
To kill him quickly here, get close enough and try to do straight stabs at him. He will parry your stab and will attempt to counter. When he does, shield bash at the right time to quickly stun him. Once stunned, stab him in the chest. After this, he will jump back and shoot off his own "skyward strikes" at you. Just dodge these or knock them back, hitting him will stun him even longer. Just repeat until the last phase in the battle.
In the last phase of the battle, he will materialize a huge sword to attack you with. The goal is to break his sword so you can hit him in the chest two more times. Here you can take your time a little bit here. If you swing at him or Shield Bash his attacks at the right time, he'll hold out his sword to block your attacks. You'll want to hit the sword in the same exact spot four times to expose the crystal inside it to destroy it. If you don't, he will counter and repair his sword.
You can only swing at it perpendicular to how he's holding it. So if he's holding it vertically, you need to swing at it horizontally. Make sure you swing at it at the side where you last hit it. If you see the broken side on the right, swing at the right. After the sword is destroyed, you can stab him in the chest.
The first phase of the Demise battle is fairly easy. Simply dodge or Shield Bash his attacks, then counter. After most of his attacks you will only be able to get in a single hit, and that is all you should attempt. If you manage to block and counter a full series of four consecutive attacks, he will be stunned, and you can wail on him for a while until he blocks you.
Occasionally during this phase, he will attempt a rapid three-hit attack with his sword. He will continue with the second slash even if you block the first; if you're quick enough to notice this and react, hit him between the first two slashes, and he will be instantly stunned.
After you hit him enough, the second phase begins with Demise charging his sword with a lightning bolt. At first you must simply concentrate on dodging his Skyward Strike. He may attack normally once or twice, but very soon he will dispel his charge in a bolt. Do not try to shield bash this bolt; simply dodge to the side.
After he dispels his first bolt, you are now competing with him for the lightning. You can only charge your sword when lightning flashes in the background. Demise will attempt to charge his sword, but if your sword is raised at that moment, you will take priority and charge yours instead. Raise your sword at every possible moment, except when you need to do a Shield Bash to block Demise.
Once your sword is charged, take the first opportunity to hit him with your Skyward Strike. He will be stunned, and you can attack him.
If Demise charges his sword a second time, you are in trouble. He will take his sweet time in dispelling his bolt from now on. Now, you must concentrate solely on dodging his next bolt, whenever it may come. He may use any number of normal attacks during this time; shield bash them, then immediately get some distance between you and him so you have time to dodge. But if you keep too much distance by constantly moving away from him, he will always do rush attacks to close the distance. Until he dispels his charge, make no attempt to attack. If you charge your sword, Demise will attack you while the charging animation takes control from you.
The first time you stun Demise with a Skyward Strike, you can attack him until he blocks you. The second time, you will knock him down and be able to do a Fatal Blow. DO NOT do the Fatal Blow on your first opportunity. He will always get up before you land your blow and your sword will stick in the ground. Demise will not attack you while your sword is stuck, but your rhythm will be messed up and you'll be more likely to lose the next lightning bolt.
After Demise gets up from being knocked over the first time, lightning will probably not be flashing right away. Raise your sword anyway, but watch Demise very carefully; he will almost always do a rush attack here, and if you do not put your sword down soon enough, lightning will strike it at just the right moment to disable you from blocking Demise.
The moment you block the rush attack, raise your sword and lightning will strike. Hit Demise with the bolt, attack him mercilessly, and this time you can do the Fatal Blow and end the battle.