If you die a couple times quickly, you'll be offered the chance to play on an easier mode.
Plus Game Modes (+)
Defeat the game on any difficulty level, and you'll unlock "New Game+" mode. With this mode, you can restart the game with all your existing data, including your demon compendium, analysis, log, fusion data, and everything else. This makes the game easier to play!
Unlock Master Difficulty
All you need to do is defeat the game in normal mode (with any ending) and you'll unlock the "Master Difficulty" mode.