Once you obtain 15 stars, go to the courtyard and the cage that leads to Big Boo's Haunt. Remember that Mario on stars 2-7 are recommended. When you arrive, enter the main mansion, go upstairs, and enter the door on the far right.You should arrive near a red ? box. Stand on top of it, and backflip or wall-kick to the 3rd floor.
Enter the door, and go into the Luigi painting after that.
What's this? You seemed to have arrived at a marry-go round maze. Instead of going back and forth, take the door to the right when you enter. This should lead you to another area. Go to the left door this time. Again, another room. Go to the right, then left. Then run like the wind until you reach 3 platforms. Get on them in order, and go in the hole.
You get into a room with a large mirror, go up to it, and King Boo will appear! Either punch him from the behind or ground pound him 3 times. He will give you a Luigi key, which opens up Luigi's door.