Eternals and Unlockables: The King of All Cosmos does not like cheaters.
Eternals
To open the "play forever" stages, build a Katamari bigger than the listed size on one of the levels below before the timer runs out.
Make a Star 4: Bigger than 1m 30cm
Make a Star 8: Bigger than 25m
Make the Moon: Bigger than 800m
Shooting Stars
To unlock the Shooting Star for a stage, you must speed finish the stage faster than the time listed.
Make a Star 1: 1 Minute
Make a Star 2: 3 Minutes
Make a Star 3: 4 Minutes
Make a Star 4: 6 Minutes
Make a Star 5: 8 Minutes
Make a Star 6: 8 Minutes
Make a Star 7: 8 Minutes
Make a Star 8: 12 Minutes
Make a Star 8: 15 Minutes
Make the Moon: 20 Minutes