Super Mario Galaxy/Freezeflame Galaxy

Freezeflame Galaxy is accessible from the Bedroom observation dome. You need 26 Stars to enter.

Star 1: The Frozen Peak of Baron Brrr
Boss fight.

Star 4 (Cosmic Comet): Frosty Cosmic Mario Race
This Star is available when a Prankster Comet is in this Galaxy.

Race a mirror of yourself to reach the Star.

Star 5 (Purple Comet): Purple Coins on the Summit
This Star is available when a Purple Comet is in this Galaxy.

You need to collect all 100 Purple Coins, with no time limit.

There are no coins on the initial planet upon which you land, so use the Pull Stars to navigate around. You haven't got much time, so try and go along paths where there are many coins in a row.

Star 6 (Hidden): Conquering the Summit
Enter Star 1.