Don’t be too hasty when navigating past the spinning square platforms at the beginning of the level. If you rush across them, you risk running right off the edge. Instead, wait until they’re spinning upward so that you can get a better angle when you jump, then land as the next platform begins to flatten out.
Stand on the screw-top at Point 4 and shake the Wii Remote to spin around and turn the screw. As you do, the purple platform you’re on rises into the air, while the one on the right drops. At the peak of the platform’s lift, drop down onto the next platform on the right.