First you need to complete the game (i.e complete world 8) then when you load your save game hold L+R and select the save file using A the game will say "Luigi" and load to the level select with you being Luigi.
Note the game does not have to be fully complete, just the last level, you can skip entire worlds if you want.
Also, after doing these requirements, you can also unlock challege mode, which prevents you from going backwards in levels, to do this pause the game while on the level selection map and press L R L R X X Y Y, a message will confirm correct code entry.
