The second time, Enkidu is a huge pain. To take him out, give someone a Nihopalaoa and hit him with a Remedy, giving him just about every status ailment. Just take him out after that, although he wont be doing much damage anyways.

Once Enkidu is dead, the fight is pretty straightforward. Buffs are a huge help, and Bubble helps even more. However, Gilgamesh is fast, and he occasionally gets 3-4 hit combos and uses Monarch Sword to dish out big damage. Just Arise and keep fighting and he will eventually go down.