The hardest fiend, or monster for that matter has to be Omega..

I vaguely remember where you deal with him at, but I believe it has to do with caves of some sort.

Oh yeah! My memory saves me...

He is the boss of Dungeon Zero: Omega

While I think he is the hardest battle, he may fall right behind Shinryuu- but still this is a hard battle.
You might need for your characters to be above level 65. This battle may take a few tries also..

Shinryuu can be easier than Omega, but you have to invest a lot of money in order to buy Coral rings to evade his initial Tidal Wave attack......

Can anyone else recommend any harder battles than this, in this game?