You need to be able to access the Star Door at the top of the stars in the main room. Go through there. *As Luigi* Enter the doorway at top and you'll find yourself in a room with a huge mirror. Grab the Power Flower and run through the mirror. You then get to the otherside and jump into the picture of Wario's face.
You need to go through a path with Bully's, platforms, and a few other things. At the end, there is a hole. Jump into it and you fight with the boss, Chief Chilly.
Chief Chilly is the boss you need to defeat to get Wario's Key.
To defeat this boss, you need to push him off of the battle area 3 times. What you need to do is to get him to go closer to the edge. When he is near, punch him or dive into him to push him off of the battle area into the bluish sea.
He'll bounce up and down and then get back onto the battle area. He'll destroy some of the outer part of the area, meaning there is less space to walk on.
Now, you'll have to do the same thing again, and he'll bounce back on the battle area, breaking the outer part again.
Not only is there little room to move, you'll have to try even harder to defeat Chief Chilly.
Repeat the same process, but as he is about to fall off the battle area, he'll stand on the edge, wobbling and trying to stay on. Punch him quickly and he'll fall off.
You will then get the key to open Wario's Door and unlock him.
Okay, I hoped this helped.