This base is surrounded by lava. There are Bill Blasters in a couple of areas. Approach the first gear and spin it. It will make the staircases spin. Rotate them so that you can access the doorway under staircase near the lone Flaptor. You'll find the first gem in there. Spin the gear again so you can go up the stairs. With good timing, approach the gear in the path of the Bullet Bills and spin it. It will rotate the Bullet Bills so you can aim them. Have the break the bricks behind them, then aim them at the bricks near the other staircase. Once all four of those brick blocks are broken, aim the Bullet Bills in the opposite direction. On the other side of the Blasters is the second gem. Return to the first gear and spin it so you can go up the other set of stairs. Drop down and you'll see two Flaptors circling three item blocks. Stand near a block to make the Flaptors hit them. One has a Super Shroom and the others have coins. Walk down the stairs to a platform in the lava. There is a Bill Blaster down here. Carefully cross along the Bullet Bill's path to another gear. Aim it on a diagonal at the moving platform with the bricks. You can't let go of the gear. Once the bricks are gone, rotate the gear so that the small set of stairs you walked down are in the position the Bullet Bill originally was. Take the platform to get the third gem, return to the rotatable path, then walk up the stairs through the doorway in the larger staircase. There is a fourth gear here. Rotate it to move the part of the base you started on. You'll see the Star, but if you keep rotating the gear, you'll find an alcove under the Star. This contains a Gold Mushroom. Rotate the Star into place, then walk to get it.
Special Challenge: Collect the Gold Mushroom.