Bowser's Dark Matter Plant is accessible from the Bedroom observation dome. You need 33 Stars to enter.
This galaxy consists of several platforms floating freely in space. Much of the space between the platforms is made of "dark matter", which will kill you instantly upon touch.
Star 1 (Grand): Darkness on the Horizon
Ride the yellow moving platforms in front of you. At the top, defeat or avoid the Dry Bones. Run over the rotating platforms (fast is probably easiest). You will reach a 2-D bit viewed side-on. Different areas in this section have the gravity going in any of four directions, with arrows on the wall showing the direction. You need to make your way across and use the moving platforms, especially the L-shaped platforms, intelligently, to avoid falling off.
Once through, climb the pole. Jump off, but watch out for the moving holes in this platform and the holes and puddles coming up. Travel on the moving pink platforms, then moving yellow platforms. Run up the wall to another 2-D bit, with more mindbending gravity. As before travel the platforms, making sure not to fall off into the dark matter. Keep an eye on the arrows coming up and position yourself accordingly.
At the end, ride the platform up. Break the crystal holding a couple of Lumas to make some stairs and continue up to the top where you will meet Bowser.
Boss fight - Bowser. This boss fight will be much the same as before on Bowser's Star Reactor, but he has more attacks like the Dark Spin in this battle.
When Bowser is defeated, collect the Grand Star, which as well as increasing your Star total will unlock the Engine Room dome.