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.
Attack from afar or move in. If you stay back, use Wakka and Lulu, plus you’ll get more support from the airship. If you move in, select your most powerful characters. Close attacks are weak but when it begins to inhale, move back or feel it’s wrath!
u should get in to the habit of starting multiple save files at intervals for 1 game this helps alot at points of no return because then u have a fall back point from before u got stuck with the boss
best strategy if ur wakka is good u should play some blitz now and get his overdrive called attack reels this can do up to 12 hits per go