Here is the full list of all 21 Mayhem Intergalactic achievements.
Win 100 multiplayer games.
Win 10 multiplayer games.
Win a multiplayer game.
Keep control of your home world for the entire game.
Use rally points to connect all planets in a Quick Start game into a single network.
Destroy 5000 enemy ships in a single game.
Destroy 5000 native ships, over multiple games.
Win a game as the red player, taking no more turns than there are planets.
Win a game without destroying any native ships.
Same as Natural Intelligence, but additionally don't lose any battles.
Win a Quick Start singleplayer game with the AI difficulty set to Highest.
Defend your last planet from an invader.
Conquer a planet named Miranda.
Conquer the home world of an opponent, but lose your own home world to that same opponent.
Destroy 2500 native ships, over multiple games.
Destroy 2500 enemy ships in a single game.
Destroy 1000 native ships, over multiple games.
Conquer 5 planets in a single turn.
Win a Quick Start singleplayer game.
Conquer an undefended enemy planet. Then win the game.
Destroy 1000 enemy ships in a single game.