Penance is an optional boss battle in the International and PAL versions of Final Fantasy X.
After defeating all of the Dark Aeons go to the airship and talk to Cid. Go to the destination chooser and you will see that Penance has opened up as a new destination. Select it and you can fight him. You will be on the airship fighting him and his arms. You can run from battle but when you return he will have full health again.
 Recommended Battle Strategy
Have the following characters: Rikku, Wakka, Tidus, Kimahri or Auron (choose 2) Have Rikku in Overdrive-ready state and prepare 2 Gambler Spirits. Equip an armour with the following abilities: Auto-Haste Auto-Protect Auto-Potion Def. + 20% and one more thing stock lots of Potion. Since you have Auto-Haste, you should get 6-7 turns first. Have Rikku mix the 2 Gambler Spirits, yielding to "trio-of-9999." Then aim for the arms, the arms will take 6 turns to kill. Once you've killed one arm, Penance would use Obliteration. Normally this would deal 11,000+ damage to all characters ] even with Protect but since, you have Def. + 20%, it should be reduced into 9,000+.
Don't worry about your health because Auto-Potion is there for that. With "trio-of-9999", potions become X-Potions. Use Cheer for 5 times (even at maxed stats Cheer takes effect). This would reduce Obliteration to only 6,000-7,000 damage. On your next turns keep Quick Hitting the arms. He should regen them after a while. Give priority in killing the arms rather than the body. When both arms are gone, that's the time you attack the body. Never let the arms get a single shot on you because they will do more damage than the body itself. Repeat this cycle and after you deal 3,000,000 damage, his lower half gets destroyed and the second half of the battle begins. *Please take note that during his first form, Penance has Auto-Protect.* The second half would be a little different.
This time, he'll use Immolation instead on Obliteration. Immolation deals more damage, normally 15,000+ to one character even with Protect status. With Def. + 20% and Cheer, it would only deal 9,000+ damage which you'll most likely survive. However, take note that Immolation also inflicts Curse and Full Break to one character and siphons all MP. Three Stars is helpful here. Just use Dispel whenever you get hit by Immolation. This round, you should be more aware of the arms because once Penance gets a turn with both of his arms present, he'll unleash Judgment Day. As said before, focus on the arms. After 40 minutes or so, Penance's attacks tend to slow down. This is the signal that he's weakening. Just repeat this process and you're on your way to victory.