This Trophy is for beating the final boss in story mode. Speaking from the perspective of someone who's beaten all of the games in the Disgaea series, I think it's safe to say that the final boss in D2 is the most difficult story mode boss to date. His fight takes place across two stages, and there's no way to save after beating the first stage. You must beat them both in one go. On top of that, the boss has an Evility on the second map where he absorbs a percentage of the stats of every person on the map, meaning you can't just overwhelm him, no matter how much you might have overleveled your party.
So what's the trick? Fight dirty! The first stage of the fight is pretty simple and should require no instructions. For the second part, do what you can to kill the pig enemies without pulling the boss himself over. With them out of the way, start hitting the boss with your strongest character and his or her best move, but make sure that they're the ONLY PERSON you have out of your base panel when you hit him. Afterwards, heal your guy as necessary, then have a tossaway character lift the boss. Now end your turn. The person who lifted the boss will die, but his sacrifice won't be in vain, as it means the boss was completely unable to attack you with his completely cheap, ohmygodhowcanhedothat attack. Just keep this up until the boss is dead!
If you try this a few times and still find yourself unable to beat the second form of the boss, I'd suggest grinding out the map of your choice for hell and improving your gear a bit. Equipment gets insanely expensive towards the end of the story, but the extra stats could make all the difference in this fight. Good luck!