Here is the full list of all 12 Battle: Los Angeles trophies - there are 7 bronze, 4 silver and 1 gold.
Complete the game on Easy Difficulty
Unlock all the unlockables
Kill 2 aliens with one Rocket
Complete the game on Hard Difficulty
Watch an unlocked video
Complete the game on Normal Difficulty
Call in the airstrike to defeat the Command Center
Complete a mission on Normal without dying, failing, restarting, or continuing campaign
Destroy the gas station
Kill 15 enemies on the HMV turret
Survive the pool attack
Kill 20 enemies with a sniper rifle