The Red Star Challenges are three mansions that appear in Luigi's Mansion 6: U Are Doomed!!. The mansions are the Soaring Sky Mansion, the Flying Field Mansion, and the Plane Playground Mansion. Based on the name, they involve the Red Star.
The challenges are only accessible once Luigi recovers the Red Power Star, which is recovered in the second mission of the Passageway Mansion, "Red Coins of the Passageway". Once Luigi enters the red door, he will access the Red Star Room. When Luigi is in the Red Star Room, he will find three more red doors with the names of the mansions on each of them. After entering any of these doors, Luigi will end up in one of the mansions.