To get to the level that contains the boss for Chief Chilly, you will need:
- Luigi
- Access to the room that has the Wet-Dry world pictures.
Once you come up the spiral staircase and through the door, turn right, and you should see a door on the with a star symbol on it. Open the door and you'll get to a room with a mirror. Jump up and grab one of the power flowers, then run through the mirror. Manoeuvre your way to jump into the picture frame that has Wario's image on it. Once you're in, go down the slide, and the wind will blow you up. You'll then land on a platform. Jump over all the tilting platforms, then jump onto the platform that moves back and forward. You'll land on the next part. Turn right and freefall you're way into the lake below. Jump over the next few parts, then find your way over the moving path that goes up, down and all around. Once you're on the next part, there are some elevating ice blocks, get your way all the way to the top. You should then see a big hole. Idiotically, jump down here.
And there you go, a big frozen Bully. Now, what you have to do, is ground pound Chief Chilly until he falls off the edge. He'll come back on and bits of the platform will diminish. Keep doing that until you're left with not much, and then he'll eventually fall off.
Note: Once you've won, you can get an extra hidden star by going through the other door in the mirrored room.