Yeah, haste is the big problem with this guy. If you can handle things up till that point, (not getting poisoned, not staying as stone etc etc) then, just before he hits the 10,000 HP mark, cast "Reflect" on him, so that when he DOES cast haste, it bounces off him and hits one of your team.
Evrae will only cast haste on itself if you take haste away from him (ie use Slow on him) so, since Reflect only bounces his spell back to you, and doesn't actually have you "take it away" he won't re-cast haste, and you'll be able to finish him off pretty easily.
Just remember these main things:
Haste Tidus / Rikku
Tell Cid to move as soon as Evrae takes a breath
Heal ANY status immediately (ie Stone, poison)
Heal any damage taken immediately
Allow Cid to use all 3 missile salvos
Use "Reflect" on Evrae before he reaches the 10,000 HP mark
After that, you shouldn't have too much of a problem.