Breaking the Laws of Gravity
This galaxy is inside a structure made out of wooden blocks with different gravities marked with arrows on the walls. From where you enter through the pipe, head to your right and drop down through the empty space filled with Paragoombas. At the bottom, jump on the flower and spin the remote to launch into the next area. The gravity starts out downwards, but when you jump past the Swaphopper, you can spin near the blue switch by the Goomba to flip gravity. Going back left toward the Swaphopper (who you can now jump on) will take you to a green warp pipe where you'll find the hidden star. Continuing on the other way, follow the line of coins to a platform that will take you down to a ledge with a Spiny Piranha Plant. Entice it to attack and move out of the way, then jump on its head when it lands, giving you access to another spin flower that will take you to the next section.
Gravity is going downward once again and you'll find a ? Coin above a slide after two Goombas. Take the slide down to the checkpoint, then jump up into the red section when the platform comes over and jump down to the blue section onto another platform. This will take you to a stationary platform with a Toad on it. You'll need to ride the next platform up, then jump over the Swaphopper and flip the switch to flip gravity. Head back to the left along the ceiling and jump the steps so you can get onto the platform. Now that you're on the other side, you can jump to the bottom of the platform on the right and optionally get the 1-Up mushroom below it. That platform will take you down to a section with rolling Chomps.
Right after a Chomp drops down and starts rolling away, jump up behind it and follow it to the right then jump the small gap. Here you'll need to get past a couple Thwomps while they're raised. In between them you can see the Comet Medal above you. The next section flips back to downward gravity with a slide down to the next checkpoint. Here you'll want to grab the Fire Flower from above and start breaking the wooden crates below to keep moving right. After a Goomba and a couple more boxes, you enter a red area with flipped gravity where you'll need to take out another Goomba and more boxes on the right. If you lose your fire power before destroying the boxes, you can wall jump back down to the Fire Flower below. When you get past the last of the boxes, keep moving to the right to hit the next checkpoint.
When you jump out onto the green section, gravity pulls you into the wall and you'll have a top-down view. Keep moving to the right, avoiding or killing Goombas until you get to back inside the blocks where gravity goes downward again. On the small patch of green that has wooden block walls on the sides right before entering the blue area, you can backflip up onto the upper wall which lets you run around on the outside of the planet. You'll find four 1-Up mushrooms here, one in each corner of the large area. Going this way also allows you to skip the Thowmps inside and go straight to the Power Star, which you can drop in on. In the section with the Power Star, there are four gravities to contend with. If you get caught up in the swirl, just let it take you around the blue section with the Power Star and press into the wall there so you can wall jump over the star.
The Great Crate Incinerator (Hidden Star)
You can find the hidden section by entering the green warp pipe in the ceiling right before where you first flip a switch to change gravity. Just backtrack past the Swaphopper after flipping the switch.
You will end up in a room with several wooden crates and a Fire Flower. Transform to Fire Mario and throw fireballs at the crate in the far right corner of the room to reveal a hidden orange Warp Pipe (there is also a 1-Up mushroom in the crates in the bottom left). Take the pipe and the Gearmo there will ask for your help destroying the all of the crates on the screen. You will have a limited time to destroy all the crates so hurry up. Remember that a single fire ball is capable of passing through multiple crates at a time. What you want to do is quickly long jump to the bottom corner of the area and move across the screen shooting fireballs up the screen so they each take out multiple boxes. You can also try using the fast fireball trick to speed up the process. Your reward is a shiny Power Star.
The first Green Star is above the checkpoint flag right after the part where you break the crates with the Fire Flower and before you move onto the green, top-down section. From the lower section on the left of the flag, jump up onto the higher section and continue on for a triple jump and spin to get the star. Alternatively, you can jump in from the top of the green section by the star and spin up to it. The second Green Star is in the room with the Thwomps right before the Power Star. Get on top of the rightmost Thwomp in upside down gravity and jump over to the Toad on the right. Above him is the Green Star that you can backflip and wall jump to. Alternatively, you can use the trick at the end of the green section to get on the outside wall and drop down into the part with the Green Star.