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