Here is the full list of all 11 Hyper Space achievements.
Get a total score of 50.000 points.
Score 2.500 points in Arcade mode.
Unlock all spaceships.
Reach level 20 in Arcade mode.
Play the Multiplayer VS mode.
Get a 50 star combo in Arcade mode.
Reach level 10 in Arcade mode.
Score 1.000 points in Arcade mode.
Get a 20 star combo in Arcade mode.
Get 100 points in Arcade mode.
Complete the Story mode.