Start the level off by walking onto the conveyor nearby (not going against it), then ducking behind the first Thwomp to get Green Star #1. Continue going around, until you can get to the other alcove. Go to the end here and get on top of the Thwomp, riding it up to the second level. Grab Green Star #2 right next to where you reached this level, then go around until you can reach the double Thwomps on the other side. Ride these ones up to the third floor, then sneak past the Bullet Bills, to the corner that has Green Star #3.
Cross the conveyor now and wait for the one nearby Thwomp to reach the top, allowing you to snatch Green Star #4. Head to the end of the walkway here, through the little corridor, and onto the Thwomp at the end. This will let you reach the very top of the course, where you need to walk along the thin pathway (watch for the Bullet Bill). When you finally get to the end, drop down the hole and you can grab Green Star #5, finishing the level.