Star 1: The Deep Shell Well
This star is pretty easy. The stage begins with a cinematic entry where Mario flies through a tunnel, lands in a cave, and the level starts. Avoid the bats as you get to a well, go in it, and slide down a slide. Once you land in the pool of water, push A repeated to swim forward. Once you encounter the spiky balls, go underwater. You can't breathe underwater. There is, however, a shell, giving you extra speed to worry less about drowning. Even without the shell there are still coins in bubbles to give you extra air, and they are not spread out. Eventually you will encounter some Snoodles, but you can defeat these with your shell's forward light. Make sure to take the tunnel to your left for a Comet Medal. Get to the hill with a low ceiling, avoid the Urchins, then break a brick wall to reveal the only eels in the level. Note that there's two of them. Pass some Snoodles and take the Launch Star. The second portion of this stage starts by falling down a pit (or long jumping on a Paragoomba for a 1-up) to get to the next section. Avoid the boos and go through rings to build up speed, then take another low ceiling hill to get to the ending sunset part. Once you are here, throw your shell (go left if you lost it) at a chest, free Captain Toad, and get the star.
Star 2: The Chimp's Coin Challenge
This Star is only available when you get a letter from The Chimp. In order to receive The Chimp's invitation you must have completed the first level. The goal of the challenge is to get 10000 points in a limited time by defeating enemies. Most enemies here can be easily defeated by shining your headlight at them. The Snoodles award 100 points each, the Gringills award 300 points each, and the Boos award 100 points each. Look for the hidden 1-Up Mushroom which is located where the Comet Medal used to be in the original mission. It is worth a big 1000 points.