BOSS BATTLE: Overdrive Sin
HP: 140,000
AP: 20,000
Weakness: none
Steal: Ether, Supreme Gem
This fight requires that you MUST use Hastega in order to win. If not, you'll have to deal with the power of his overdrive, which will almost certainly kill the entire party. If by chance he does get off his overdrive, try to have an Aeon in there to take the blow. Better yet, use Yuna's Grand Summon on an Aeon to unleash two overdrives in a row. In general, use all of your strongest attacks as fast as possible and try to move in all party members to get the great AP.

Source: http://www.evermynd.com/ffxwalkthru.html

And from my personal experience try using Overdrives, equip Celestal Weapons and cast high damaging spells(prefebly Black spells) and use high damaging moves.