Super Mario Galaxy/Good Egg Galaxy

Good Egg Galaxy is accessible from the Terrace observation dome, and is the first galaxy available to you once you reach the Observation Platform.

Star 1: Dino Piranha
Run between the fences on the left, to the underside of the first planet, and up the side of the tower. At the top, talk to the Luma, who will turn into a small Launch Star. Perform a Spin Attack to reach the bigger Launch Star, then spin again to be hurled towards the second planet, in the shape of a dumbbell.

On the second planet, you need to collect five pieces of a Launch Star, while avoiding the rolling rocks. Watch out for the muddy areas on the ground, which considerably slow down your movement. Activate the Launch Star by spinning, to reach the third, bean-shaped, planet.

Here you can touch the ? Coin to produce some Star Bits to collect, which will give you a hint on which way to go. To proceed you will need to defeat the Piranha Plant, and a Sproutle (vine) will appear. Climb the Sproutle by spinning to reach the fourth planet.

This planet looks like a hollowed-out apple, and is the first one which will kill you if you fall off it into the black hole in the middle. Avoid the spiky plants and rolling rocks and proceed along the path. At the other end of the planet, you'll find a giant Piranha Plant, which can be destroyed by spinning into one of the rubbery green plants so that the plant hits it. Watch out for your aim, though, because if the green plant misses the Piranha Plant, it will spring back towards you and knock out some Star Bits you are carrying. When the Piranha Plant is dead, a Sproutle will appear.

Use the Sproutle to reach the fifth planet, which is another bean-shaped one with a stone structure on it. Climb the structure, defeating the enemies along the way, until you reach the top. There you will need to spin to destroy the crystal and release a Launch Star. Fly off to the final planet, where you will meet the boss, Dino Piranha.

This is your first boss fight of the game. To defeat him you will need to spin his heavy-looking tail into his head, so that it flies up into the air and hits him on the head. You will need to do this a total of four times. Each time he will get angrier and chase you, so try and avoid his attacks.

If you need to replenish your health during the boss fight, as well as the obvious coin trapped in a crystal which you can destroy by spinning (or which the boss will destroy as he chases you), there are also a couple of what look like glowing carrots on the ground. Shoot these with a Star Bit to release a coin. Watch out for these carrots in other levels.

Star 3: King Kaliente's Battle Fleet
Boss fight.

Star 4 (Speedy Comet): Dino Piranha Speed Run
Available when a Prankster Comet is in this Galaxy. Do the same as for Star 1, only within a 4 minute time limit.

Star 5 (Purple Comet): Purple Coin Omelet
Available when a Purple Comet is in this Galaxy. Collect 100 Purple Coins scattered about the galaxy, with no time limit.

Star 6 (Hidden Luigi): Luigi on the Roof
This is one of the Hidden Luigi Stars, available after Luigi sends you a letter with a photograph of this galaxy. The title of the Star gives Luigi's location away, but like all the hidden stars you don't actually see the title of the Star until you obtain it.

Luigi and the Star are on the roof of the house on the first planet, accessible via the orange pipe on the underside of the planet. Talk to Luigi to obtain the Star.