Ohohoho. Some of the bosses in P3 are pretty hard. Monster battles can go bad too if you get caught off-guard; expect to die a few times in P3.
It's somewhat classical RPG combat: your character (protagonist) can Attack, cast Magic (the magic of the Persona, that is), Defend, etc. Your spells and element weaknesses/strengths depend on your Persona. Personas are found and fused, and there's tons with various spells and elements. The best Personas obviously come with time and crafting.
The sim part is really enjoyable. If you are picturing something like the Sims, in which manipulating one's life is a chore, P3 is nothing like it: having a social life, and deciding when to study and when to fight is actually a lot of fun and adds a lot of depth and enjoyment to the game.
EDIT: If you want a truly hard RPG, P3 FES is your game, according to Zew.