To unlock Asagi mode, at the title screen, highlight the "New Game" option, and press TRIANGLE, SQUARE, CIRCLE, TRIANGLE, SQUARE, CIRCLE, X. In the Japanese version, press TRIANGLE, SQUARE, X, TRIANGLE, SQUARE, X, CIRCLE. Alternately, collect all the various Torn Letters hidden throughout the game.
Use the following trick to unlock the Prinny raid skill easily. Restart the game by going to the Runaway Shop. Select the "Hell's Finest" difficulty. Choose the Moab Fortress, and proceed until reaching the Boss. Allow the game to idle here to lose 1,000 lives in approximately two hours.