Complete the main storyline, then complete the following task to unlock the corresponding bonus dungeon.
Blacksmith Stove: Examine the blacksmith's stove.
Bufu Cave: Complete Master Rank of the Battle arena.
Dragon Veins: Examine Yotsume Rock.
Hidden Path: Complete Master Rank of the Battle arena.
Karakuri Inn: Examine Yotsume Rock.
Mysterious Dungeon: Talk to the WIS Staff in the tavern.
Shirne of Mystery: Talk to the WIS Staff in the tavern.