Extra Map 1:
Beat the game.

Extra Map 10 and Baal:
Beat Extra Map 9.

Extra Map 2:
Beat Extra Map 1.

Extra Map 3, Etna, and Flonne (Fallen Angel form):
Beat Extra Map 2.

Extra Map 4:
Beat Extra Map 3.

Extra Map 7:
Beat Extra Maps 1-6.

Extra Map 8:
Clear a random dungeon with 50+ floors, with Level 500+ enemies on the bottom floor, and have unlocked Extra Map 6.

Extra Map 5 and Laharl:
Beat Extra Map 4.

Extra Map 9:
Clear a random dungeon with 99 floors, with Level 1000+ enemies on the bottom floor, and have unlocked Extra Maps 6 and 8.

Mid-Boss:
Beat Extra Map 5.

Myao:
Beat Extra Map 8.

Pringer-X:
Complete the game and clear all the extra levels.

Extra Map 6:
Clear a random dungeon with 30+ floors, with Level 300+ enemies on the bottom floor.