Konishi from the development team explains in the PsOne version you must level up in a dungeon before fighting a boss. As long as you raise your levels a bit while walking through a dungeon you can beat a boss in Persona 2: Innocent Sin on PSP if you play the game on normal difficulty.
The probability of instant death attacks and bad status effects sticking to a character have been tweaked too. Meguro joked that people would break their PSP if they threw it in frustration. Finally, events with time limits have been fine tuned, as well.
If it sounds like Atlus softened the game too much Persona 2: Innocent Sin has a hard mode and an easy mode. The PSP version has three difficulty settings, which you can change from the configuration screen anytime you’re at a camp.