Onward towards a strategy. I know you've all pretty much posted what I'm about to, but you've left out some key tricks:
First, buy Softs and Antidotes from Rin and customize Stone and Poison Ward onto your armors. These will also help you in later battles. Now, when the battle starts, do as the other people said and cast Slow on Evrae, and when it's Tidus' turn again, cast Haste (or Hastaga if you have it) on your characters. Have Rikku use a Smoke Grenade on Evrae. (Note that any status inflicted by a "Use" item (such as the aforementioned Smoke Grenade will always inflict its status. Just a little side information.) Now, have Auron use Power Break on Evrae. After this, scan him to make sure that Power Break and all other status ailments mentioned have been induced onto him. If not, simply repeat. After all of this, Evrae is what one might call a weakling. Of course, use Al Bhed Potions when needed (and have some extra Softs incase Rikku gets Petrified). You can pretty much take care of him now as you wish. When he gets down to 12,000 HP, he'll use Haste. Whatever you do, DO NOT COUNTER THIS. If you do, Evrae will recast Haste, and get another turn to attack. When Evrae gets down to about 9,000 or so hit points, if Rikku's Overdrive is filled, have her mix a (I believe) Grenade, and any Stat Sphere (such as a Strength Sphere, HP Sphere, MP Sphere, etc.), as that should cause 9,999, giving you a nice, juicy Overkill. Make sure everyone at least defends once in order to obtain AP.