Here is the full list of all 27 Starsphere achievements.
Take a look at the options
Collect all achievements
Collect all the stars on each level
Complete all the levels in stealth mode
Find all the secrets in each level
Complete all the levels without the use of checkpoints
Get 3 stars rating for each level
Lose...
Buy everything in the Starmarket
Destroy Supernova
It's nice to be a millionaire
Unlock all levels
Complete level 1
Complete level 2
Complete level 3
Complete level 4
Complete level 5
Complete level 6
Complete level 7
Complete level 8
Complete level 9
Complete level 10
Complete level 11
Complete level 12
Complete level 13
Complete level 14
Complete level 15