If you want to fight the most difficult enemy in the game, make sure your active party is at least at level 70 or higher, with Bubble Belts equipped to double your HP. This enemy, the Hell Wyrm, is located in the Sochen Cave Palace in a secret room.

To find it, you have to first speak to one of the toad creatures on the summit of Mt. Bur-Ominsace, who will talk of a Wyrm Philosopher. From there, head to Balfonhelm and speak to the man in the bar who will also talk about the philosopher. Next, head to Cerobi Steppe, and speak to the Moogles working on the windmill, who will reveal the philosopher. The philosopher will, in turn, hand over a key.

With the key in hand, head to Sochen Cave Palace, to the Destiny's March section of the map. Do the puzzle there (where you have to run around a track in a certain order, much like Final Fantasy VI's light puzzles). If you do it right, a prompt will tell you a door has opened. Head to the Ascetics Door on the west side of the map, which was the door that was opened. Head down the path and use the key on the next door. Inside is the Hell Wyrm, the game's most difficult enemy.