Yu Yevon is the final boss of Final Fantasy X. It is fought in Sin's core after defeating Braska's Final Aeon and all of Yuna's aeons. The battle against Yu Yevon is more of a "cinematic" final boss though, and Braska's Final Aeon is often cited as the game's true final boss.
Yu Yevon's main offensive attack, Gravija, an attack that even harms himself, removes 75% of the party members' current HP, and thus cannot KO. He can also use a party-wide Osmose and Ultima, but only when his HP is low.
All party members have permanent Auto-Life (supposedly bestowed by the fayth to help Yuna defeat Yu Yevon) so losing the battle is impossible, unless one does so deliberately by petrifying themselves. The real hindrance to beating Yu Yevon is that he automatically casts Curaga on himself every time he takes damage, which restores 9,999 HP, and as in the previous battles, the Yu Pagodas will occasionally heal him.
The Yu Pagodas combine around Yu Yevon, and then they dissolve in the same way as Chaos in the original Final Fantasy after his defeat. This is the first time this style of death is used since Safer∙Sephiroth in Final Fantasy VII.
One strategy is to ensure that characters are equipped with weapons with the Break Damage Limit ability. The other trick is easier: Yu Yevon is susceptible to the Zombie, which can be inflicted with Zombie Attack. This way, restorative items and spells, including those of the Pagodas and Yu Yevon's own Curaga, will harm him, whereas resurrecting items and magic will kill him instantly. Reflect can also be cast on Yu Yevon to redirect his Curaga spells to the party, allowing the party to attack him with physical strikes until he dies.
Another strategy is to Doublecast magic for two 9,999s (or more with Break Damage Limit) every turn. Yu Yevon will only be able to use Curaga for one 9,999.
Limiting the healing potential of his Curaga spells is also an effective way of defeating him. Using Magic Break halves the amount Curaga heals. If coupled with the use of Shell on Yu Yevon, the healing potential drops to around 2700.
Another strategy requires no abilities whatsoever. The trick is to focus on keeping the Yu Pagodas incapacitated, while Yu Yevon slowly whittles down his own HP with his Gravija spells. Once the spells start doing 0 damage to him, it means he is down to 1 HP, and can be killed by any attack.
It is possible that Yu Yevon's boss fight was supposed to be a puzzle battle, where the party has to use the last strategy indicated. If so, the programmers made the mistake of not making him invulnerable to status ailments and effects, which would have forced the party to use that strategy (unless they have the Break Damage Limit ability).