At Epic, esp. epic gestalt, you can literally win the game. Power goes all the way from 'archmage who is a god' to 'fighter who fights slightly better than a level 10 fighter'.
So, pick a power level and go nuts. If you want to 'compete' you should probably be immune to everything, not rely on buffs or have a way to not get your buffs dispelled, have good mundane defences (AC, saves, iron heart surge etc), have good non-mundane defences (miss chances, immediate action teleportation etc). Movement speeds of all kinds, stuff that bypasses dimensional locks...
If you want you can go the Clone route and have lots of you. Simulacrums, astral projection etc.
Have ways of instantly killing things in multiple ways, and of bypassing immunities. Have some fun weird ways of killing people nothing defends against, like 120% real phantasmal killers etc.
You literally have room to checklist every 'win' condition, and still have fun things like Body Outside Body or a plane of infinite sharks that you throw people into.