First go to Big Boo's haunt. In the mansion, triple jump up to
the second floor.
Go in the far right door. Get the power flower. Bounce up to the 3rd platform.
Go in the door and jump into the Luigi painting. It's a puzzle. The way to answer it
is on the map. The yellow lines are doors. For the first one go in the right door on the map. (don't turn the camera). Then go in the top door of the map. Then the right door
again. Then the top door again. Cross the bridge and jump onto the first green platform.
Then jump on the second one. Then jump onto the third. It will bring you up to the top.
Jump into the hole. To beat the Boss, go behind it and punch. Repeat the process until
the Boss gives you a key. That is Luigi's key. That is how you save Luigi in Mario 64.