First, finish the game with any ending to get the boss rush mode (as a new option at the title menu). After getting the boss rush mode, play through it at least once. Then, from now on, when turning on the game or when resetting it, wait for Konami's logo screen to appear, and press UP, UP, DOWN, DOWN, LEFT, RIGHT, LEFT, RIGHT, B, A. Now the character for the boss rush mode will be changed to Simon (8-bit version) until you reset or turn off the game.