Unlock "Wayne Manor"
To unlock the "Wayne Manor" bonus level, you must achieve the rank of "True Hero" on each of the 15 hero levels. As you collect studs, the progress bar at the top of the screen will fill up. Become a "True Hero" by collecting enough studs to fill the meter. You get studs by killing enemies, opening containers and interacting with the environment; you lose studs when you die. You can also buy power bricks in the "Batcave" that will multiply your score. Once you've unlocked "Wayne Manor," travel to the section of the "Batcave" where the vehicles are parked. Go to the far right and ride the elevator to the bottom of the memorabilia room. Find the entrance to "Wayne Manor" in the top left corner.
Defeat "Wayne Manor"
To defeat "Wayne Manor," you must collect one million studs. You will only find purple studs on this level and must collect all 100 to win. Many of these studs are hidden in a side-scroller mini-game. Access the game by heading left from the beginning, destroying the garbage cans then assembling a computer. Switch to "Tech Suit Robin" and access the computer. To collect the 47 studs hidden in this game, you will have to break all of the blocks. Gray blocks can be destroyed by almost anything, brown blocks can only be damaged from the bottom, blue blocks have to be hit with a sonic gun, and shiny blocks require explosives. Another 50 purple studs are hidden on the mansion grounds. Roll a bomb into each of the spinning orange targets to collect the studs. Search the rest of the manor to find the few remaining studs.
Unlock "Arkham Asylum"
Unlocking the "Arkham Asylum" bonus level is similar to unlocking "Wayne Manor," except you must attain the rank of "True Villain" on all 15 villain levels. Once you've done this, head over to the "Batcomputer." Walk right, then head down the ramp and pull the lever. Head through a door on your right and find the memorabilia room in the corner. Ascend the ladder to access the "Arkham Asylum" bonus level.
Defeat "Arkham Asylum"
To beat this level, you'll once again have to collect a million studs. Earn four purple studs in the gym by kicking a bomb into one of the goals and using the center button to reset it. You can also get three purple studs by running on the treadmill. Experiment with various vehicles in the garden maze to make studs appear. The rest of the studs shouldn't be difficult to locate, just be thorough.