This is one of the hardest normal bosses in the game. And at this point in the game, depending how you dealt with the sphere grid you might be in a lot of trouble.
There's three phases to the boss.
To start with you should have all character's overdrive gauge maxed, you should also max all the aeon's gauges. And if you have any celestial weapons, that's better (I had the weapon that corrosponds to bahuamut's power but it was not required).
There's a lot of ways to deal with this fight, depending on your builds, but this is how I handled it.
Stage one is a pretty straight fight. She has 20k hp, and she'll fight decently hard. However Lulu using Firaga Fury on her which should be easy to deliver on will make stage 1 short as heck. It's worth it because Stage two and three will take more out of you and the fury attacks will never do more damage than in the first stage. I had a strong wakka who attacked to help finish off stage one. If you have Hastaga, use it. Twice the attacks for the whole battle is DEFINITELY worth it.
Stage 2 she grows and gets 48k of health. This is a harder battle, however I was lucky I had two characters (lulu and Rikku) with Holy. Holy on a primary magic user (lulu or yuna) delivery 9999 damage every time. On Rikku it was over 6000. Not bad, but not great. In addition she'll zombie your team. This is NOT a bad thing, though deal with it as you will, however when she's low on life make sure your whole team is zombies. You'll thank me later. If you can add in reflect on your team it'll help as well. Also feel free to use character overdrives here. Save the aeons.
NOTE: If you are a zombie, potions hurt you. ETHERS also will hurt your magic. Don't use any healing or magical improving items on a zombie.
If you got past stage 2, you're still in trouble, Stage three takes stage 2 and adds in the worst attacks. She may have been casting Curaga on you before, she'll continue to do that, but when she starts stage three she'll use her worst attack. Mega Death, which instantly kills any human... except zombies. You can have death proof gear if you already have it. If not, you are going to have to stay as a zombie for the battle. This sounds a lot harder than it is. however she will also cast curaga on you, and regen, neither are good spells to have if you are a zombie.
At stage three it's up to the user. Either continue to use holy (cure the zombism, and then give turbo ethers to get your MP back), beat her down (melee is relatively effective), use overdrives, or Switch to aeons. Aeons will do a lot of damage, but she can still kill them easily and potentially drain them (healing her) That being said 9999 damage is 9999 damage, and can help kill her. My bahaumet who was damage broken was hitting 12000 which i used as a final blow.
Overall if you beat this battle you'll have beaten one of the hardest bosses in the normal game. There's not much left of the story, but you will also earn the ability to get the airship.
In addition after killing her, you may want to go down the steps in the back and then open the chest, for the sun crest. If you don't do that, a dark Aeon will block the path and until you beat him (and he's a harder boss) you won't be able to unlock tidus' weapon.