In the room with Chef Kawasaki, use Cook's Cook Pot to clear all of the enemies. The Rare Picture Piece is located in the water.
Go to the room with the drain pipes. Have two characters with Parasol perform the Chumbrella Friend Ability to block the water flow and have a character with Fire light the fuse to the dynamite; alternatively, one can use Ice or moves with the Blizzard element to freeze the water instead of using two parasol wielders. The explosion from the dynamite will reveal a round-trip door.