Here is the full list of all 20 Interstellar Conquest achievements.
Destroy an enemy ship for the first time.
Destroy 10 Small Size Hull ships.
Destroy 10 Medium Size Hull ships.
Destroy 10 Heavy Size Hull ships.
Capture a planet for the first time.
Use a wormhole.
Get hit by an Ion Storm.
Win against an easy enemy.
Win against a normal enemy.
Win against a hard enemy.
Build a factory.
Build a planetary defense.
Build a market.
Build a Fighter ship.
Build a Bomber ship.
Build a Gunboat ship.
Build a Destroyer ship.
Build a Cruiser ship.
Build a Battleship.
Build a Carrier.