Dark Aeons

From Final Fantasy - Wiki on Neoseeker

In the PAL Version of the game there are optional bosses known as dark aeons. They are exactly as the name says, they are evil versions of your aeons, controlled by the monks of Bevelle. The good thing is that unlike your previous aeon battles, you can actually summon the same aeon that you are facing. The bad thing is however that to defeat them you will need a fully customised sphere grid, which can be a hard thing to do. It is possible to defeat them using a non-customised grid, however it is very hard, and you will find it difficult to beat the ultimate uber boss of the game Penance.
Penance is just as it sounds, the hardest optional boss in the game and will take over one hour to beat (not an exaggeration). You shall see why in a bit. To fight him you must first defeat all dark aeons and then it will appear as a location on the airship.

NOTE this is only available for the PAL version of the game.

For more in depth details about Dark Aeons, please visit the Dark Aeon FAQ by Steaver370.

There is a VERY quick, easy and painless way to beat the dark aeons which I shall tell you, however I recomend that you beat them by fighting normally as it is much more fun.
All you have to do is get Yojimbo from the Cavern of the Stolen Fayth and then pay him exactly 1/3rd of your gil and he will 98% of the time use Zanmato which WILL kill any Dark Aeon, Boss and Penance. However I consider this cowardly and so again I recommend that you beat them in your own way.