Mana Khemia: Student Alliance
This game is titled Mana Khemia: Student Alliance in North America and Europe, and Mana-Khemia: Gakuen no Renkinjutsu Shitachi Portable in Japan.
Successfully complete the game to unlock New Game+ mode. You can access a bonus dungeon at the start of the Chapter 9. To find it, walk past the room with the Chimera Boss battle via the Old Schoolhouse in Chapter 8. The bonus dungeon is at the previously locked door at the end of the dungeon.
Strategy guides from GameFAQs