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