Professor Layton and the Diabolical Box
After beating the game, go to the Top Secret section of the Bonuses menu. You'll be able to access an art gallery depicting various scenes from the game.
Character Profiles List
After you've beaten the game, go to the Top Secret section of the Bonuses menu. Inside, you'll be able to access profiles for every character in the game.
Layton's Challenges: The Sweetheart's House
Under the Bonus Menu, you'll find an option called Layton's Challenges. These challenges are comprised of espcially difficult puzzles. They can only be unlocked by fulfilling specific criteria in the main game. One of them is called the Sweetheart's House, which contains Puzzles 148, 149, and 150. In order to access it, you have to beat the 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.
Top Secret Options
Once you acquire enough Picarats, you unlcok the following options in the top secret section
To earn a Golden Icon next to your save file, complete the following criteria.
Concept Art Collection
After you've completed Professor Layton and the Unwound Future, you'll be given a special code. These codes are unique for each DS system. Copy down that code, access the Top Secret bonuses of Professor Layton and the Diabolical Box, select the Hidden Door menu, then select the Ticket To Time Travel option. Input the code, and you'll unlock a collection of concept art.