If the below directions aren't clear enough, then listen.
1. Insert your coin(s).
2. Select One Player Puzzle Mode.
3. Select either character.
4. When the Stage Select screen comes up, hold the Start button and rotate the joystick clockwise(Up, Up-Right, Right, Down-Right, Down, Down-Left, Left, Up-Left) three times in a row.
5. The map screen should change from brown to purple, and your character should say something. Now the puzzles are harder than before!