Here is the full list of all 18 Starscape achievements.
Particle lasers
Zone 4 complete
Nova bomb
For rescuing 25 missing crew members
Zone 3 complete
For rescuing 20 missing crew members
Drone weapons
Zone 2 complete
Ion weapons
For rescuing 15 missing crew members
Zone 1 complete
For rescuing 10 missing crew members
For rescuing 5 missing crew members
Defensive shields
Zone 5 complete
Game completed on easy difficulty
Game completed on normal difficulty
Game completed on hard difficulty