Here is the full list of all 25 Interplanetary achievements.
Defeat an enemy planet.
Fire Solar Laser superweapon.
Fire Asteroid Diversion superweapon.
Fire all the superweapons during the same turn.
Unlock all technologies.
Grow five cities to their maximum populations.
Win an online multiplayer match.
Win 5 online multiplayer matches.
Win 10 online multiplayer matches.
Win 50 online multiplayer matches.
Win 100 online multiplayer matches.
Win 10 single player games.
Win 100 single player games.
Beat the Impossible AI.
Win an online multiplayer match with at least two players.
Win an online multiplayer match with at least four players.
Win an online multiplayer match with eight players.
Destroy 100 cities over any number of games.
Defeat two enemy planets in one turn.
Build 200 buildings on your planet.
Hit your own planet with a railgun.
Win a match with barely any population left.
Have your planet run out of material.
Have 25,000 material in stock.
Produce 7,000 Energy in one turn.