Here is the full list of all 15 StarShip Constructor achievements.
Destroy a pirate ship
Destroy pirate ships,total CP achieve 20000
Build a spaceship,cost more than 4500 CP
Your ship has more than 3000 Armor
Complete a mining process
Build a spaceship,cost more than 10000 CP
Build a spaceship,cost more than 20000 CP
Mining more than 500 units
Destroy pirate ships,total CP achieve 50000
Destroy pirate ships,total CP achieve 100000
Get 50000 Credits
Get 1000000 Credits
Unlock all construction modules
Died 10 times
Reach galaxy core