Super Mario Galaxy/Deep Dark Galaxy

Deep Dark Galaxy is accessible from the Garden observation dome. You need 46 Stars to enter.

The main planet has a beach and an underwater section past a gate. There are also a couple of smaller planets.

Star 1: The Underground Ghost Ship
For the time being, ignore the shell you will find underwater, as that will lead to the Hidden Star 6.

Boss fight.

Star 4 (Daredevil Comet): Ghost Ship Daredevil Run
This Star is the boss fight from Star 1, with just one life point.

Star 5 (Purple Comet): Plunder the Purple Coins
100, no time limit. In ghost ship area. Some in water behind you at start. Some you'll need to crouch jump for - look for shadows. Need to jump out of water for some.

Star 6 (Hidden): Boo in a Box
Enter Star 1. Use shell underwater to destroy mines.