The first full collection is 120 stars as Mario. Finishing the story alone leaves the hidden stars, comet challenges and later Luigi rescues to complete.
Finish the main observatory route
Collect stars from the Terrace, Fountain, Kitchen, Bedroom, Engine Room and Garden. Clear the Bowser or Bowser Jr. boss associated with each newly opened section. Feed the Hungry Lumas to open their separate galaxies, and return to a dome whenever a new mission or comet icon appears.
Hidden and comet stars
A hidden star can branch from a mission you have already completed. Use the chapter’s named hidden-star route rather than replaying only the main objective. Check the Prankster Comets separately: speed, daredevil, fast-foe and Cosmic Mario challenges award their own stars. Purple Coin missions become available after the story ending and each supplies another star.
Luigi’s rescue letters
Rescue Luigi in Ghostly Galaxy, then check his letters and photographs at the observatory. The three rescue locations are Good Egg, Honeyhive and Battlerock. Find him at the pictured location and complete the rescue; simply finishing that galaxy’s main story is not enough.
Unlock Luigi as a playable character
Collect all 120 stars with Mario, then defeat Bowser again and complete the ending. Speak to Rosalina to access the Luigi adventure. Luigi has a separate star collection and different movement; repeat the full 120-star set, including his own rescue and comet missions.
The last star for both characters
After both 120-star runs and the required final-boss ending, visit Grand Finale Galaxy through the Planet of Trials. Collect its 100 Purple Coins once per character. The final collection is 121 stars as Mario and 121 as Luigi.