This trophy is for defeating the new hard mode dungeon bosses. The hard mode dungeons unlock after completing the game once. After completing the game, you can return to any of the dungeons outside of Mount Vellenge to have the option of playing a harder version of the level. While you can play multiplayer, only certain dungeons are available on certain days of the week. However, in single player you can play them at any time.
To prepare, I'd recommend getting most of the artifacts in the game, the best weapon and armor available to you, and elemental resistance accessories. These new dungeons are no joke, without near max defense enemies will do a ton of damage. They also like to cast freezing or stunning magic attacks, some of which are -aga spells which take up the entire screen. It also doesn't help that there are three times the amount of enemies than in the normal dungeons, so be expected to get ganged up on.
The easiest of the new dungeons is probably the Falling Leaves Path, which is the hard variant of the first dungeon. Aside from the first and second locked gates, you can run to the end of the level easily. The boss is mostly the same from its easier counterpart and there aren't any particularly hard enemies assisting it. Hopefully with high stats, you should have no issues fighting it.
Regardless of your method, beating any one of the new bosses will award you your trophy.