Note: This game is also titled Professor Layton And The Lost Future and Layton Kyouju To Saigo No Jikan Ryokou.

Successfully complete the indicated task to unlock the corresponding option at the "Top Secret" menu:

Additional Character Profiles: Solve all 168 puzzles.
Character Profiles: Collect 4,200 Picarats.
Character Voices: Collect 5,000 Picarats.
Game Music: Collect 4,700 Picarats.
Movies: Collect 5,200 Picarats.
Story Art: Collect 4,500 Picarats.

Successfully complete the indicated task to unlock the corresponding Layton Challenge in the "Bonuses" menu:

The Hotelier's House: Successfully complete all ten toy car courses.
The Messenger's House: Successfully complete all twelve parrot delivery errands.
The Puzzle Keeper's House: Successfully complete 165 puzzles.
The Storyteller's House: Successfully complete all three picture books.
The Time Traveler's House: Successfully complete the game.

Successfully complete Professor Layton And The Diabolical Box to get a system-specific code. Enter the "Top Secret" menu in Professor Layton And The Unwound Future, select the "Hidden Door" option, and enter the code.