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 a Railgun (Campaign)
Complete 10 missions using the Prowl Rider PA-Gear
Defeat 100 enemies using a Laser Cannon (Campaign)
Defeat 100 enemies using a Sword (Campaign)
Defeat 100 enemies using a Grenade Launcher (Campaign)
Complete 10 missions using the Heavy Striker PA-Gear
Defeat 100 enemies using an Energy Thrower (Campaign)
Stop one enemy's attack during a mission using the Heavy Striker's E-Field
Defeat 100 enemies using a Minigun (Campaign)
Defeat 100 enemies using a Laser Rifle (Campaign)
Complete 10 missions using the Jet Lifter PA-Gear
Defeat 100 enemies using a Sniper Rifle (Campaign)
Defeat 100 enemies using a Shotgun
Travel 2,000 meters during a single mission using the Jet Lifter PA-Gear
Defeat a total of 3000 enemies (Campaign)
Complete the story
Earn a cumulative total of 15,000 Energy Gems
Defeat 100 enemies using a Missile Launcher (Campaign)
Play a mission during which a vehicle you requested gets destroyed (Campaign)
Defeat 100 enemies using a Rocket Launcher (Campaign)
Complete 10 missions using the Trooper PA-Gear
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
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)
Complete a mission without receiving any damage
Perform 30 E-Dodges using the Trooper PA-Gear
Travel 200 meters without touching the ground in a single mission using the Prowl Rider PA-Gear
Resurrect a total of 10 players
Use a field support item (Campaign)
Complete a mission with a reward of 0 at the Result Screen
Destroy a "mysterious machine" (Campaign)
Recover 55 M.I.A. drones
Play Mercenary for the first time
Earn the Title of Ensign in Mercenary
Complete 1 mission on the Hardest difficulty level (Online)
Complete 1 mission on the Disaster difficulty level (Online)
Complete 1 mission on the Disaster difficulty level (Offline)