It also gives you a chance to use the Bragging Rights Reward on something more significant than Mooks, allowing you to see just how powerful it really is ( or isn't). It also can be very satisfying when you can walk up to that boss who had you tearing out your hair last time and crush them like a bug on a windshield. Plus, it is always nice when you don't have to grind yourself numb to make the character the badass hero that they are supposed to already be.
Another possibility is making the hopeless boss fight at the beginning of the game anything but, and getting a nice bonus reward for beating the Final Boss Preview. A more basic reason is getting over the initial 'hump' of the First Town playthrough. Indeed, playing through the game twice or thrice may be the best way to power up so you can face the Bonus Dungeon. The main reason for this can be so the player has a shot at things like multiple pathways and Multiple Endings.
New Game Plus is the option of starting a new game by accessing a previous finished game, allowing you to start with improved stats, new costumes or items won beforehand.
