Super Mario Galaxy/Buoy Base Galaxy

Buoy Base Galaxy is accessible from the Kitchen observation dome. You need 30 Stars to enter.

This Galaxy's main feature is a floating tower half-submerged in water.

Star 1: The Floating Fortress
Your objective is to climb the tower, but you won't be able to do that until you release the weight underneath which is keeping it partially submerged. So dive in and make your way down below the tower. The weight is surrounded by a glass cage, and you need to get a Tornado Ted to follow you and break it.

Once this has been done, the tower will rise to the surface and you should do the same. Start by climbing onto the platform to the left of the yellow floats. Use Wall Jumps to climb up. Defeat or avoid the pink Goombas, and run under the Thwomps and past the Water Shooters. You can turn the Water Shooters off by standing on a valve and spinning. This will also release a Topman which you can use to reach the next platform, although it is possible to get up there without using the Topman.

Stand on the blue screwhead and spin. This will start the platforms above moving. In this section you will need to use the moving platforms to travel around the tower to collect five Star Chips. One is on top of one of the Thwomps below, and one is above the top of the tower - use the spring to reach it.

Once all five Star Chips are collected, they will create Pull Stars. Use them to reach the spherical planet above the tower. There are devices on each pole of the planet which emit circular pulses which you need to avoid. Go to the top of the planet, jump on the screwhead and spin, to open up the top half of the planet, which is full of water. Swim down and collect the Star below.

Star 2 (Hidden Green): The Secret of Buoy Base
This is one of the three Green Stars, which you need to collect to unlock the Trial Galaxies.

Enter Star 1, and dive underwater. Swim around until you locate a pipe protected by a glass cage. Get a Torpedo Ted to break the glass cage and enter the pipe.

You will emerge outside, on a walkway on the underside of the planet. If you fall off the walkway you will find yourself in the water again, in which case you should re-enter the pipe. Run along the walkway, avoiding Bullet Bills, to reach the centre. Allow a Bullet Bill to follow you and break the glass cage, where you will find the Star.