Play the final level, Wisdom Headquarters, and advance until you have activated the main elevator.
Go to the library (located on the unrestricted side) and go up the stairs. After you've activated the main elevator, the door at the top opens. Proceed up the stairs and out onto the balcony. Jump across onto the chandelier, then onto the other balcony, and enter the room on the other side.
In the room, there are two enemies that can be easily defeated along with the third and final piece of paper in the game. Retrieve the piece of paper and letters will come on the screen telling you that you've unlocked Boss Battle Mode in the Bonus menu. You can access this mode by entering "Bonus" on the main screen and entering your file.