Here is the full list of all 32 Space Quiz achievements.
Tutorial finished
First planet conquered
Buy the first ship in the Stellar Port
Finish a battle without losing any ship
Finish first recollection
Conquer all the planets from a sector
You have destroyed 50 ships
You have destroyed 100 ships
You have destroyed 250 ships
You have destroyed 500 ships
You have recollected 1000 units of Fuel
You have recollected 2000 units of Fuel
You have recollected 3000 units of Fuel
You have 5000 units of Fuel
You have extracted 500 units of Minerals and Fuel
You have extracted 1000 units of Minerals and Fuel
You have extracted 5000 units of Minerals and Fuel
You have extracted 10000 units of Minerals and Fuel
You have 100 ships
You have 200 ships
You have 400 ships
You have 500 ships
You have conquered 50 planets
You have conquered 100 planets
You have conquered 250 planets
You have conquered 500 planets
Conquer a planet in every sector
Finish easy level
Finish medium level
Finish hard difficult
Finish expert level
Keep all the planets under your domain