The best thing to do is to put Sin on hold and do some sidequests, such as Celestrial Weapons, and getting all other aeons if you haven't done so. Unlocking the Celestrial Weapons makes your Aeons more powerful. Leveling up works also.
Before battling Sin, you should have Yuna in Overdrive, along with your Aeons. Summon an Aeon that has Damage Limit Break. Bahamut, Anima, and Magnus Sisters automatically come with this. All other aeons will require a Celestrial weapon to break the damage limit.
Once Grand Summoned, wait until you get into range, and unleash the aeon's overdrive. Since you Grand Summoned an Aeon, it can use it's Overdrive TWICE (cause you had a full bar before.)
mrgreen
If Sin isn't down, whip out another Aeon and blast him with their overdrives. Those Aeons that can only do 9999 damage on overdrives should be last.
The best Aeons for this job when I did this was Anima (Found at Baaj Temple) and the Magnus Sisters (Requiem Temple). I did a lot of leveling up such as doing sidequests and getting everyone's Celestrial Weapons with the Sigils and Crests needed to unlock their power.
If this doesn't work, level up some more. Going to the Omega Ruins and leveling up there will really help you out.