I'll try to be concise with this.
If you're heavy into magic, Lulu and Yuna should be fixtures in your party. For me, Lulu was doublecasting Ultima and level-3 elementals, and Yuna had learned both Holy and Ultima. Added to her aeons, this basically made her the ultimate badass. From there, you can do the following:
-Get enough ultimate weapon crests to enable most of your aeons to exceed 9999 damage. This actually doesn't take that long.
-Get your aeons, and your characters, into overdrive before the battle starts.
-As soon as you enter the battle, have Tidus cast Hastega.
-Make sure you're far away from him, and use Yuna's overdrive to Grand Summon an exceptionally strong aeon, most likely Bahamut or Anima, and overdrive twice on him. This will probably take off at least 2/3 of his health.
-Send the aeon(s) away and start blasting Sin with your strongest spells. He'll drop in no time.
-Repeat for the other side using whatever aeons you've got left; use an Ether or two on Lulu to keep her MP up.
Once you get on top of Sin, you'll find that the guardian to the gateway inside doesn't really have that much health. Use Tidus, Auron, and Lulu with as many overdrives as possible to smash his ugly face in, with the occasional healing backup from Yuna if necessary.