At the end of World 2 when you are infiltrating X-Death's castle, immediately before you reach X-Death's room you will encounter a chest with nothing in it. When you leave this room, Gilgamesh will attack you. However, if you do not open the chest in this room, you will not have to fight Gilgamesh.
IF you have plenty of soke bombs and sleeping gas, use Rikku close up to use them on Evrae. It will take away over 700 HP.
In Phoenix Tower, after every few stairs you will reach a room with two pots, one on each side of the room. One of the pots contain money, but the other contains a monster. The enemy is called "Magic Pot" and will not attack you. He will say "Gimme Elixer". Use an Elixer on him and he will reward with 100 ABP and an item. This is possibly the easiest way to master items like Mimes, Samurais, Chemists, and Ninjas.
Go into these doors in order: Left, Left, Right, Left, Left, Right, Left, Left, Right, Left, Left, Right, Right, Left, Right, Left, Left, Right, and Up.
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