Requirements & Hints.

Grandmasters with the Stitched Furoma Map Piece hunt here.

There are only four mouse types to be caught here, and three of those can only be caught using specific cheeses. Ensure you have collected enough tokens from the students downstairs to craft the required cheeses: Susheese, Glutter and Combat, to catch the Masters of the Cheese Claw, Belt and Fang.
Be warned, these are strong mice, requiring a strong trap. One of each Master will give you the shards necessary to craft an Ambush Trap, which may be a big help...