Star Ocean: Till The End Of Time

The Urssa Cave Temple is accessible after you complete the game, return to Crosell's lair and head to the northeastern room at the top. Next to the chest in the room is a door, go through and it you'll be in the Urssa Cave Temple. This dungeon is actually very short in comparison to the other dungeons you've traversed, use this map to help you make your way through the cave. When you reach the end of the cave, you will have to face a mirror version of Fayt and an ally he is with (will be dependent on the ending you receive).

Fayt Breakdown:

Fayt's Level: 170
Recommended Level: 130's

This fight is actually pretty unique, as the second opponent you will have to face is solely dependent on the ending you receive. The one ending you don't want is for Fayt to end up alone, as this will cause you to have to fight Luther and Fayt at the same time for this battle: it's as bad as it sounds. Fayt's possible partners include all existing party members. Because there are so many possible fights that could happen, I'll detail the general strategy against Fayt.

In short, Fayt is absolutely dangerous. He has most of the Battle Skills that you do, a faster movement speed, and the ability to "touch of death" combo you. You need to get rid of him as quickly as possible, I recommend using Dimension Door with Fayt, as it chips at both his MP and HP (an MP kill is preferable here). Your party should have fully synthed equipment at this point, so defense shouldn't be an issue. Still, this is a tough fight no matter how you look at it. Below is a video showing how I defeated Luther, if you were unfortunate enough like myself to get that ending:

Once you defeat Fayt, the trophy will unlock. (Credit to noypi_gjd for the Cave Map)