Lynels are extremely strong enemies compared to how early you'll find them in the game (for a lot of playthroughs).
If you want to know how to defeat the Lynel because you're looking for a challenge or you need to kill it I'd recommend the following things:
Have a shield equipped
You don't need to use a one handed weapon but having a shield can be extremely useful since it blocks all the damage in a risky situation. Lynels can hit extremely hard and blocking those 6-10 hearts of damage is an absolute lifesaver (especially early).
The loading screen tips are absolutely right: Don't just run into a monster over and over again but try to prepare for the fight with some elixirs and buff-food. Depending on your health you can run defensive boosts but usually you should go for shock resistance, damage up and speed up.
Have lots of weapons
2000 HP is no joke. If you want to kill this thing with your melee weapons some of them will break. If you're still in the early game multiple, maybe even all your weapons will break. Keep that in mind when fighting this guy. You don't want to find yourself in a situation where your only option is using bombs.
Learn to side-hop, or backflip his attacks
ian_itor has already pointed this out in his answer but I want to mention it again since it's probably the most important thing when fighting Lynels. Dodging and counterattacking are extremely efficient. The attacks are slow and predictable. If you get the timing right you can land a lot of free hits with Flurry and it's great practice for dodging in general.
Aim for the head/use special arrows and Chuchus
If you want to use ranged make sure to aim for the head for a stagger and increased damage but also don't be afraid to use special arrows and elemental Chuchus. Freeze, shock and fire are your allies in this fight. Each element has it's own advantages and they can make the fight a lot easier when used correctly. Also be sure to not stand in a puddle and pop a lightning resistance elixir when going for a ranged method.
To kill the Lynel only two of the above mentioned points are required: A lot of weapons and good dodging. The others I've mentioned are additional help and are available from the start. I've excluded points that are unlocked since it's very possible to find a Lynel before you have access to certain advanced gadgets or powers. Obviously the fight gets easier the more you progress into the game because of better weapons, armor and powers but if you follow these steps you'll be able to kill the Lynel with little health and a bit of patience and practice (doable with Zora weapons and about 4 hearts).
One final note:
If you simply want to complete a quest with a Lynel near the objective, I'd highly reccomend checking if you can't just sneak around it since the rewards are usually not worth the trouble they cause (at least in the early game).