Layton Kyouju to Kiseki no Kamen

In the game's Top Secret menu, there is a section called The Hidden Door. One of its options can only be unlocked by using a 3DS system-unique password found in the Hidden Door section of Professor Layton and the Last Specter. It gives you access to a bonus conversation between the cast, as well as a brief quiz about what happened in the previous game.

Layton's challenges are the hardest puzzles in the game. They are found under the bonuses section. Each one has a different way of being unlocked.

If you manage to completely clear all of the aisles in the Shop mini-game, you'll unlock the Medal of Completion in your catalog.

Once you acquire enough Picarats and beaten the game, you unlock the following options in the Top Secret section of the Bonuses Menu.

After you've completed all of the Toy Robot stages, you'll unlock the Hidden Maze in the middle of the world map. The Hidden Maze contains an additional set of stages.