I would recommend not using aeons overdrives until you know that youv'e only got about 1 or 2 moves left to fit in - otherwise you will have your aeon losing turns while it recovers, instead stick to putting out your long distance attackers first.(remember to have all of you characters overdirive guages full!) I used Lulu, Wakka and rikku so that whilst the airship is being pulled towards sin you can still hit him without waiting for him to get his overdrive up without you even engaging in combat. Keep wakka doing his ball attacks while Lulu casts her most powerful magic from afar. Rikku can just be there as a support for now as she cannot hit sin in the first three turns with her items. I should also point out that you shouldn't use your overdrives at all yet. As soon as sin is within close combat range I would recommmend bringing out the beefy characters - I swapped Lulu with Auron, Wakka with Tidus and kept rikku on.
With these characters I started slamming sin in the head with sword attacks (it'd be really good if you have quick hit with tidus to fit in more attacks).
I now used Rikku's overdrive to make a super mighty g (2x chocobo feather) which casts protect, shell, haste and regen on every character. Now you should be fitting in as many attacks with your two strongest characters as possible (DON' HESITATE TO USE AURON'S ARMOR BREAK ABILITY BECAUSE SIN IS NOT IMMUNE TO IT), feel free to swap rikku for another hard hitting character right now because she isn't really needed any more seeing as you have protect, regen and shell.
Contine to attack with moves which you know will deal the most damage until Sin's overdrive bar is about 70% full. NOW is the time to unleash all of your characters overdrives before sin wipes you out for good....as I said - do tidus' and auron's most powerful overdrives then keep swapping over to your other characters to unleash theirs too.
Hopefully you have dealt around 115,000-120,000 damage points to sin, if you have then immediately switch any of your characters to Yuna before sin's overdrive bar is completely full. GRAND SUMMON YOUR MOST POWERFUL AEON and then unleash their overdrive straight away. Bahamut should deal about 25,000 with anima and the magus sisters dealing even more. This should wipe out sin's head just in the nick of time.

If you find that your characters are not hitting for enough damage even with armor break status on Sin then you are going then there is no other choice than to train more unfortunately. However this battle plan is fairly accurate to my first playthrough of the game with a very average party so it should be ok.