Super Mario Galaxy 2/Upside Dizzy Galaxy

Star 1: A Walk on the Weird Side
When you finish this level, a pipe will appear on Starship Mario which will lead to a Luma Shop.

Star 2 (hidden): Burning Upside Dizzy
Enter Star 1. Enter the pipe early on in the level. Talk to the Gearmo.

When you finish this level, a Fire Flower will appear in the engine room on Starship Mario.