I managed to beat this boss on the 15th try as a melee character. There are two attack dogs and one Capra Demon (who has good attack range and an unblockable attack) in one tiny room.
How can a spell-casting character win this fight, considering the casting time needed for most spells?
Run up the stairs to the left of where you enter, and follow the walkway round - you can successfully snipe him from the end of this ledge whilst dodging most of his attacks. If he does manage to hit you, drop down and run back up again to get a few more shots in. You will need to take out the dogs first though, they make this fight really annoying if you don't, given the small space you have to fight in.
Repeat till he is dead!
Before fighting the Capra Demon you should free Griggs of Vinheim, who you'll find trapped behind a locked door shortly before the Capra Demon fight. Unlock the door using the Residence Key, which is sold by the Male Undead Merchant in the Undead Burg, and he'll go to Firelink Shrine. Once he's at Firelink Shrine you'll be able to buy spells from him, as well as two rings which make your sorceries more effective.
The spells you want to buy from him for the Capra Demon fight are:
Aural Decoy: This spell will aggro nearby enemies, causing them to attack it instead of you. This will actually work on the Capra Demon and the Dogs, so it's extremely helpful during the fight.
Great Soul Arrow: Stronger version of Soul Arrow.
Great Heavy Soul Arrow: Similiar to Soul Arrow, except it deals over double the damage of it, and takes longer to cast.
As soon as you enter the boss fight immediately cast Aural Decoy. You'll actually have enough time to cast this before the Capra Demon and Dogs make their first attack, so you don't need to worry about being killed off right at the start. You should then one-shot each of the dogs using Great Soul Arrow. After the dogs are dead, keep casting Aural Decoy so the Capra Demon will attack it instead of you. While it's busy attacking empty air, damage it with Great Heavy Soul Arrow. You should have enough casts of Great Heavy Soul Arrow to kill it, but if you don't just fall back to using Great Soul Arrow to finish it off.
I'm surprised nobody has said this, but you can actually whip explosive oil and dung over the entrance to the Capra Demon room and pick off the dogs (and even the demon himself if you want) before you enter. A little sneaky, but necessary if your character considers 3-vs-1 a little unfair!
Recently I beat the Capra demon with a caster and here's how.
This seems a little too simple, but seriously, try it: as soon as the fight starts, do a roll directly to your right.
Examining the room, you can see that near the entrance (hidden by the camera when you enter ) is a weird little corner that makes it impossible to jump to the left and creates that annoying "Hey there! You're dead!" effect that Capra Demon tends to create.
The object in this fight is absolutely to make it to the stairs. When you are on the stairs,
In other words, to win this fight:
Get to Stairs > Kill Dogs > Kill Capra Demon
Odds are Capra Demon is going to kill you before you get to the stairs, if you get there at all. Once you roll, keep your shield up and move quickly around him in a circle, and then back up the stairs.
Easier said than done, as you'll probably be taking some heavy damage! As I've said before, the real secret in this fight is to do a sudden jump to the right when you enter the room.
Don't wait for the Capra Demon or his dogs to attack or anything. Just move swiftly for the stairs.
Bonus Tip: You can get to the Capra Demon much faster by unlocking the door at the bottom of Lower Undead Burg and going to fight him via the female merchant who sells moss.
Run up the stairs and blast the dogs. When the Capra Demons starts walking up the stairs drop down through the ledge. He should follow by jumping allowing you to get off a shot or two when he lands before you need to repeat the process.
In my experience walking out the ledge doesn't protect you from his unblockable attack. For a pure spellcaster it is fatal so don't stay on the ledge other than to allow you time to take out the dogs.
In my Soul Level 1 (Pyromancer) playthrough I managed to beat the Capra Demon by first using a Rapier augmented with Charcoal Pine Resin to defeat the dogs, then using spells to kill the demon itself.
I used the same general strategy as recommended by soulBit:
However my choice of character build presented its own challenges.
Taking out the dogs is much easier if you use a weapon that allows you to keep up your shield as you strike (eg. spear, rapier). My character couldn't use any of them because of the Dex requirements. I ended up using a rapier anyway, because, even though my stats were not high enough for its use, it did not slow down my attack animation (as the spear did when I tried it). I applied the Charcoal Pine Resin so I would still do damage.
The toughest part of the battle was getting to the ledge. It took me many tries to get past the demon and the dogs just so I could climb the stairs. Don't give up trying.
Once the dogs were dead, I shot soul arrows at the demon, only stopping to raise my shield when the demon had climed the stairs. After it strikes it usually falls off the stairs, giving you an opportunity to heal and resume spell casting. Keep this up and his death is your reward.
This is one fight where, as a spellcaster, you can benefit greatly from taking advantage of summoning in allies to help you fight. Enter the room, and dodge the monster long enough to allow your (hopefully melee capable) white/gold summons to engage the dogs, and attract the ire of the boss; you can then contribute by shooting the boss with your spells, and using your Estus Flasks strategically to keep your allies alive and fighting.
