Hmmm, well, the first obvious thing to do would be to train. Try getting to a couple of health [can't remember what they're called] before entering the battle. I had a problem Evrae a while back so I'll just tell you what I did...
Use the characters that you find the strongest &/or easier to use. As you probably know you HAVE to have Rikku & Tidus in your party & so the other character is free of your choice. I personally alternated between Lulu & Auron [Lulu for range, Auron for close combat].
While Evrae is close attack with Tidus & possibly Auron/Kimari [you chose]. Be sure to use their limits because they can deal some serious damage [expecially Auron's]. When Evrae attacks be sure to keep your hp up but DON'T let it go below half way point. I found Rikku's Al Behd potions very useful here [I think they can cure about 2,000+ health at a time]. So make sure you stock up on those before entering the battle.
When Evrae huffs that's the signal to get Tidus/Rikku to say Fall Back. In a matter of 2/3 turns the airship will fall back at this will prevent Evrae's most powerful attack, Poison Breath. Now, I think it happens automatically but Rikku's dad will launch some missiles at the poor beast which again will deal some serious damage. Right, this is the time Lulu/Wakka comes in. Use Lulu's magic [I think Bizzard spells do the trick] or Wakka's Dark Attack [this will blind Evrae making his/her physical attacks inaffective].
Be aware though. Sometimes, after falling back, Evrae swoops closer to the airship attacking your party. If so, cure & show him/her some steel. And so remember, the huff is the signal. Repeat the process until dead [if I remember right this can be a lengthy battle, so make sure you have the time].
If that isn't helpful you could try checking out:
http://www.gamefaqs.com/console/ps2/game/27609.html.
Edit:
I just remembered that Tidus's Haste ability is really useful in the battle. It allows you to attack a lot faster than normal making the battle easier & quicker. And also, if Evrae uses Poison Breath [his most powerful attack, the one you're trying to stay away from] cure fast & use one of two remedies/antidotes. To add to that use a soft if Evrae cast Stone Gaze on a character.