You will need to call down the Hungry Luma to Starship Mario and feed it 300 star bits to open up this galaxy.
Think Before You Shake
This course takes a great deal of manual dexterity to complete. Each time you do a spin attack, the floor panels flip over, alternating between red and blue. Rolling Chain Chomps follow defined paths and are knocked off the course if their panel is flipped out from under them. In some cases, the Chomps can be lifted back up onto the play field by a poorly-timed spin attack. A good way to traverse this galaxy is to jump to an empty panel and spin in the air so you land on it when it flips over. Try this out along the panels heading to the first platform with two Goombas and an Octoomba on it.
In the next part with the electric fences running across the panels, flip them so red is showing, then take the path they create. After you get through the first fence, you can flip and get the 1-Up mushroom on your way. When you get to the next electric fences, you can either long jump over to the next red panels, or more safely jump and spin and take the blue panels. At the end of the next set of red panels, jump through a gap in the fence and flip to blue, then take the two more blue panels through another gap to the next platform with a checkpoint flag on it.
In the next area a Chomp will come rolling out on the far side of the red panels and follow them around the turn toward you. All you have to do here is stand on the first blue panel, then jump and flip to red right after the Chomp falls and you should have enough time to make it to the other side and jump to the next platform. In the next section Chomps will roll on either color, so you have to be more careful. Start out on red, then run jump and spin to switch to blue and run across them right after the Chomp drops. Follow the blue panels and jump out to the lone blue panel with the 1-Up mushroom on it. When you see the closest Chomp fall through the red frame, jump and flip to red then jump to the two red panels on the left. When the Chomp next to you falls through the blue frame, jump and flip right where it fell through, which will drop the Chomp on the red panels coming toward you. Quickly jump across the single blue panels to the platform, collecting the Comet Medal along the way.
The last area is a narrow series of panels with electric fences going through them and then the platform with the star. Flip to red and jump out to the first panel to start. From there jump through a gap in the fence to the next red panel, then jump and flip to blue and go through another gap. Jump and flip to red on the other side, then jump diagonally off the next red panel to the blue one, flipping in the air. Jump and flip back to red, then jump through a gap in the fence and flip to blue at the same time. From there you can jump to the platform and claim your Power Star.
Purple Coin Flip 'n' Sprint (Prankster Comet)
This time you'll have three minutes to collect every purple coin on your way through the galaxy. You'll want to be very good at jumping and flipping so you don't fall through, but other than that, it's just the same as the first star, only timed. You'll get a 1-Up mushroom on the first platform you get to, so don't worry about dying during the run, just go for it. To save time, avoid flipping to a panel right next to you if you can avoid it. You can jump a single panel with a normal jump and two panels with a long jump. The only really tricky part will be collecting coins where the Chomps are. When you see a Chomp coming, jump to the other color before it gets to you and flip. You can immediately flip back if you need to after it falls through.
Green Stars
After you cross the first set of panels and get to the platform with the enemies on it, flip to red and you will see the first Green Star's shadow on the third red panel away from you. You can either triple jump or backflip and spin to grab the star. If you're backflipping and spinning, do it facing away from the blue panel next to you so you have something to land on if you miss the star. In the set of panels where the Comet Medal was after the checkpoint, you'll find the second Green Star. Standing on the blue panel with the 1-Up mushroom on it, the star is above the red panel the closest Chomp falls through. After it falls through, jump and flip to red, then quickly get under the star and backflip and spin.