Sin will charge towards the player on their airship, moving slowly forward turn by turn while opening its mouth. After about sixteen turns, Sin's mouth will open completely and it will use its Overdrive, Giga-Graviton, to destroy the player's party, resulting in a Game Over.
For the first half the battle, Sin is out of range of physical attacks. Its only attacks, outside of the massive main attack, are status effect moves. It is not possible to protect against Giga-Graviton, as it bypasses damage altogether and simply causes a scripted Game Over. Even summoning an aeon will not prevent this.
Aeons' Overdrives are useful in removing Sin's HP before it can destroy the player's party. If Lulu can do so, doublecasting Flare or Ultima is effective. Auron should use Armor Break to make Sin vulnerable to attacks, and Tidus should cast Hastega on the party and use Quick Hit, which can allow him several attacks in a row.
It is possible to end the battle quickly by having Rikku mix a Trio of 9999, wait until Sin is in range, and use multi-hit attacks such as Tidus's, Lulu's or Wakka's Overdrives. A strong Anima's Overdrive can KO Sin in one hit.