On the moon you will meet CosMc, who will inform you that the force of gravity is very low there. He will also tell you that if you find at least five cards of his puzzle, he will show you where Hamburglar is hiding. However, you should already be in possession of one of his cards.
Level 1 - Moon Monsters
As the name suggests, there are some very dangerous lunar monsters in this level, sprouting from mounds in the ground. If they grab you you will immediately lose a life, so be careful. Take advantage of the fact that here you can jump very high, thanks to the low gravity, to overcome them. That said, the level is fairly linear. Shortly after the start, there is a suspended platform with many arches. Keep going until you come to a rocky wall just after a sign with an arrow pointing to the right. Climb to the top and take a long jump to the left. You will find a card to collect in the sky. Then go back where is the sign. Here is a secret passage that allows you to pass through the lunar ground (like in the clouds in Birdie's Treehouse). You will come to an area with two 1-Ups and a card suspended in the void above a dotted platform. Jump on them without taking them and reach the right wall. Here too there is a secret passage. You will then find a fill-in block. Go back and place it on the platform. You can thus collect the card and the extra lives without dying. Exit this hidden area and continue to the right, until you reach the finish line. Thanks to the very long jumps you can make here, getting to the right of it won't be a problem.
Both cards you found are for CosMc's Retreat.
Level 2 - Swisserland
A labyrinthine level. Here, however, the force of gravity is normal. Head left immediately and drop as low as you can. Then proceed to the right removing the blocks you will encounter and at the bottom you will find a 1-Up. Go back, go up along the same path and halfway up go right. Follow the path. When you arrive at a large space, you will have to make a jump in order to take the tunnel on the right. If you fail you will have to go back and try again. Once done, you will come to a zipper. Enter it to take you to another area of the level. Go right and remove the block at the bottom of the hollow to find another 1-Up. Go back and go right. Jump over any gaps you find and eventually you will find a card. Grab it and remove the blocks you just passed. You will end up straight on the finish line. Unfortunately here, taking the Golden Arch to the right of the line is almost impossible.
The card you found is for CosMc’s Retreat.
Level 3 - Constellations
A vertical level. In front of you, you will see a row of springboards. If you climb on them, you will jump incredibly high, due to the low gravity. But first, go to the right side of the level and walk under the springboards. On a rise you will find a card. To get it, you'll have to make a very tiny jump. If you jump too high, you will inevitably end up on the springboards, which will catapult you high. Keep trying until you succeed. After grabbing the card, jump high using the springboards. You will have to be careful to avoid the flying monsters. Above you will find other small moving springboars. Also jump on these to climb higher. The finish line is exactly in the middle of the level. But stay on the sides and jump onto the springboard above it, avoiding the reversers. At the top right you will find another card to collect, while on the left there is a zipper. Entering it will lead you to a bonus level. Here you will simply have to climb by collecting the arches. At the top you will also find two 1-Ups. Then enter the zipper just below to return to the main level. Head to the finish line and jump on it. Taking the Golden Arch to the right of the line is difficult, due to the reversers and low gravity.
The first cart you found is a secret card and the other is for CosMc’s Retreat.
Level 4 - Spring Fever
Another vertical level, but from top to bottom. There are three pairs of blocks on the floor. Under each of them there is a hidden passage. It is advisable to take the one on the left: remove a block and drop down. You will end up on a ledge. Here too there is a hidden hole in the floor. Drop down, but move as far to the right as possible. You will land on a small ledge with a zipper. Enter it and you will be transported next to a card. Grab it and drop into a hole in the floor again. At this point, you will need to avoid the springboards as you fall, as they will catapult you up again. The finish line is at the bottom of the level. Try to land on the blocks to the right or left, to remove them and easily reach the line. Taking the Golden Arch here is practically impossible.
The Card you found is for Cosmc’s Retreat.
At this point, you should have all six of CosMc’s cards. Go to his house and he will tell you that Hamburglar is hiding inside a volcano. You will then automatically return to earth. Going back to CosMc now that you have found all of his cards is useless: he won't give you anything.