Super Mario Galaxy/Good Egg Galaxy

Good Egg Galaxy is accessible from the Terrace observation dome. You need 1 Star to enter.

Star 1: Dino Piranha
Boss fight. Spin into Dino Piranha's tail, so that it flies up into the air and hits him on the head. Repeat a couple more times until you defeat him.

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.