The second confrontation with Gilgamesh is a lot tougher than the first one. The combination of Gilgamesh's attacks and that of his dog Enkidu's can be quite lethal.
Some tips to help win the battle more easily are:
1) Do Dispel/Dispelga on Gilgamesh and his dog first to get rid of their buffs.
2) Then put his dog to sleep and blind it. Also cast oil on it. The Nihopalaoa + Remedy method should get these done conveniently.
Then spam Firaga on it. Magic doesn't wake up foes/characters like melee attacks do. Because the dog is in Oil status, he will take much more damage from the Firaga spells.
Some recommended gambits for the battle are the following. You should set these up before the fight:
Set one of your characters gambits to:
Foe: Status = Sleep>Firaga
Foe: Party Leader's Target>Attack
This is to defeat the dog first.
Then set your other two characters gambits to:
Foe: Highest Max HP>Attack.
They will only attack Gilgamesh.
Having Bubble/Bubble Belts are necessary as Gilgamesh tends to hit hard. Use Decoy on your main tank/damage dealer, so that he takes most of the hits. Have Curaja Gambits set to keep HP at 50% or above. For optimal speed in bringing KO'ed guys up, have one use Arise and 2 others use Phoenix Downs. Have Esuna/Esunaga gambits ready for his Lvl X. status attacks. It's also recommended to swap the proper gear on-demand to provide immunity for a given status condition before it snags one or all of your guys. When he puts up any palings, turn attack gambits off during that period and then turn them back on when it expires.
Steal during 4th and 5th phases in order to obtain the Genji gear.
Hope this helps anyone who's struggling with him.