Here is the full list of all 14 Super Mutant Alien Assault trophies - there are 12 bronze, 1 silver and 1 gold.
Kill the galaxy 1 boss.
Kill the galaxy 2 boss.
Kill the galaxy 3 boss.
Beat the game in one run on normal difficulty, by yourself.
Beat the game in one run on heroic difficulty, by yourself.
Beat the game in one run on epic difficulty, by yourself
Defeat a boss in under 10 seconds.
Keep a booooomerang in the air for 30 seconds.
Wipe out an entire monarch flock with one sniper bullet.
Kill 6 enemies with one sniper bullet.
Make a gas ball travel at high speed.
Unlock all equipment.
Use your pulse belt on a cooking explosive.
Activate 30 pressure machines with explosives.