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