Here is the full list of all 22 StarSmashers achievements.
You started your journey as Captain of the Space Beagle.
You upgraded the Space Beagle.
You upgraded the Space Beagle, again!
You upgraded the Space Beagle, just look at those cannons.
Fully upgraded the Space Beagle.
Fully upgraded the Diffuser weapon.
Fully upgraded the Tactical Laser weapon.
Fully upgraded the Pulse Cannon weapon.
Fully upgraded the Multi-Ray weapon.
Finished the tutorial.
Defeated Kaldor Seth's henchmen before leaving the Aquila system.
Defeated Kaldor Seth's henchmen before leaving the Cetus system.
Escaped the Hydra system.
Defeated Kaldor Seth's henchmen before leaving the Ventaci system.
Defeated Kaldor Seth's henchmen before leaving the Ceros system.
Defeated the Leviathan before leaving the Hydra system.
Cornered Kaldor Seth in the Dracos system and took him down.
Fully upgraded the Mantus Missile.
Fully upgraded the Mithra Missile.
Fully upgraded the Europa Missile.
Fully upgraded the Phoenix Missile.
Fully upgrade the EMP Missile.