You can't use Aeons Silver, as theres no Yuna in this fight With Evrae. Remember :D
First thing you could do as Silver mentions Overdrives, make sure all your party members are in overdrive. fight some monsters that are on your ship before heading to where Evrae is if they aint.
They key to the battle is have everyone hastened, have Rikku use Al Bhed Potions, and have everyone at least at 1700 HP to survive the Poison Breath..
Poison Ward or Proof will come in handy for this battle for that Poison Breath thats causing you problems if you have it,. Use Slow on Evrae then Haste or Hastega on your party.
If you dont have Hastega, Just cast Haste on Tidus and Rikku, becasuse these are the only two who can use the Trigger Command to tell Cid to move the ship closer or further to the boss.
Evrae will eventually use Haste on itself when its HP is getting low, which may cancel the previous Slow you did. A good thing to do you can have Wakka try to blind it too. and yes Power Break comes in handy.
Like Silver said about Cid, he can help you here , If you ask him to pull the airship away at the right moment (right before Cid's turn), Cid will then attack Evrae with the airship's missisles on his next turn. Dont forget Cid appears in your list of characters in this fight only in the menu to the right.
The missile attack wont cause Mega damage damage though, and then Evrae will probably counter attack and use Swooping Scythe.
It uses this when far from the ship; it will fly back to the ship and hits all your party before being next to the ship again at close range..
You have probably experienced the stone gaze, so having Stone Ward or Stone Proof maybe a good idea .
Its other attack is called Photon Spray, a non elemental attack that hits randomly around 8 times. This attack happens either when Evrae is close or far. When it uses Inhale, it will start a counter for its Poison Breath attack. Make sure you heal fast because Poison Breath will Poison all your party!
If you pulled the ship away when it was charging for its Poison Breath, you will get a message saying "Too Far For Breath", meaning he cant attack you with this attack at the moment .
OK. When you pull the ship away, dont forget that you wont be able to attack it with short range attacks! So you'll have to use magic or Wakka.
Another thing, Evrae is strong against the 4 elemental magics ,Fire, Lightning, Water and Ice, so use your strongest ones if you want to damage it with magic. so You should also keep Lulu's Fury for when the boss is far away.
. A WORD OF WARNING..
I wont spoil to much...But When you defeat Evrae and you hit on Bevelle there are no save spheres to restore your characters HP after the Evrae fight until later on, But before that you have to defeat the gaurds.
WARRIOR MONK They attack with their guns and cause some physical damage. Just beat them with physical attacks. No need to waste all your magic on them. if you want you can try to blind or put them to sleep, but its really not necessary. WARRIOR MONK (Flamethrower) When you meet a battalion of Warrior Monks, defeat these ones first because they are the ones who will cause most damage. With their flamethrower, they will deal great Fire damage to all your party. If ealier you stole many Bomb Cores from the bombs, now is a good time to customize Fireproof armors. With this, their flame attack will cause 0 HP damage to you!.
YKT-63 Gaurd, He's the "Butt" Kicker read on you will see what i mean. It will accompany 2 Warriors Monks (Flamethrower). Dispatch it quickly if you can because it might "kick one of your characters out of the battle" This will happen if you kill the Warrior Monks first, being the only one remaining, he will use his Thrust Kick!. bring Lulu in, this machina is weak against Fire and Water. Other than that, it will use physical attacks on one character by slamming his heel on you. Just use magic or physical attacks, whatever you want, but defeat it first.
. Kimahri can learn Thrust Kick if he uses Lancet on them.
YAT-99 This machina will stand in the back row and you cant hit it before you have defeated the Warrior Monks standing before, in the front row. It will, however, be able to attack you from back there with its missiles and hit all your party for high damage. Like the YKT-63, it is also weak to Fire and Water. You can use this in your advantages to hit him in the back row even if the Warrior Monks are there. It has, a strong Magic Defense, but you should have Watera and Fira at this point, so use it.
Anyhow Enjoy (For Me) wasone of the best parts of the Game....