Your goal for this star will be to get to the top of the mountain, but you will pretty much start at the very bottom. When you gain control, run past the Goombas near the start, then Long Jump over the two gaps. Note that if you miss the first jump, there will be ground below you, but the second jump has no safety net. Just past those two jumps will be some mushrooms, but you can safely ignore them and follow the path around them. The next area will have a bunch of Monty Moles harassing you by tossing rocks. This is where the path can split a little bit, as the ledges by the Moles can lead you past a later obstacle if you continue straight.
For now, continue straight past the Monty Moles and you’ll encounter some Bob-Ombs. These aren’t threatening at all, but the Chuckya beyond them might grab you. Of course, you can ignore it completely and make your way to the bridge, then jump to the next section, which has an Ukiki (monkey) and Fly Guy. The Ukiki is harmless, unless you grab it, as it will steal your hat. Since this ledge isn’t very large, the Fly Guy might shoot some fire at fire and cause you to run off it. The normal way to advance is to use the giant log to reach the next ledge, but you can also use the flight from jumping on the Fly Guy to reach the same ledge.
The next obstacle on the trek to the summit will be a hill with iron balls rolling down it. Once you get near the top, you can stick to the wall to avoid getting hit. Slide down the slope after the iron balls and Long Jump the gap by the waterfall, then quickly move past the Fwoosh (cloud) enemy before it blows you off the mountain. You will eventually reach an ivy patch with some more Goombas, then a purple switch. This does nothing for you right now, so ignore it and cross the thin ledge by the waterfall beyond it. There will be one final slope before the summit, where the star is waiting for you.