Here is the full list of all 44 EARTH DEFENSE FORCE: IRON RAIN trophies - there are 32 bronze, 7 silver, 4 gold and 1 platinum.
Defeat 100 enemies using an Energy Thrower (Campaign)
Defeat a total of 3000 enemies (Campaign)
Complete a mission with a reward of 0 at the Result Screen
Earn a cumulative total of 15,000 Energy Gems
Defeat 100 enemies using a Railgun (Campaign)
Complete 1 mission on the Hardest difficulty level (Online)
Use a field support item (Campaign)
Complete 10 missions using the Prowl Rider PA-Gear
Play a mission during which a vehicle you requested gets destroyed (Campaign)
Travel 200 meters without touching the ground in a single mission using the Prowl Rider PA-Gear
Complete 10 missions using the Heavy Striker PA-Gear
Complete a mission without receiving any damage
Defeat 100 enemies using a Missile Launcher (Campaign)
Defeat 100 enemies using a Laser Rifle (Campaign)
Defeat 100 enemies using a Minigun (Campaign)
Stop one enemy's attack during a mission using the Heavy Striker's E-Field
Complete 10 missions using the Jet Lifter PA-Gear
Destroy a "mysterious machine" (Campaign)
Defeat 100 enemies using a Grenade Launcher (Campaign)
Travel 2,000 meters during a single mission using the Jet Lifter PA-Gear
Defeat 100 enemies using a Rocket Launcher (Campaign)
Defeat 100 enemies using a Sword (Campaign)
Defeat 100 enemies using a Sniper Rifle (Campaign)
Complete 10 missions using the Trooper PA-Gear
Perform 30 E-Dodges using the Trooper PA-Gear
Defeat 100 enemies using a Shotgun
Play Mercenary for the first time
Defeat 100 enemies using an Assault Rifle (Campaign)
Complete a mission in which not a single NPC ally retreats due to damage (Campaign)
Complete the prologue
Unlock all trophies
Complete the story
Reach 10,000 Hit Points
Purchase all items
Purchase all customization parts
Obtain all weapons
Earn a cumulative total of 1,000,000 Credits
Defeat 100 enemies using a Satellite Weapon (Campaign)
Defeat 100 enemies using a Laser Cannon (Campaign)
Resurrect a total of 10 players
Recover 55 M.I.A. drones
Earn the Title of Ensign in Mercenary
Complete 1 mission on the Disaster difficulty level (Online)
Complete 1 mission on the Disaster difficulty level (Offline)