Here is the full list of all 44 G.I. JOE: The Rise of Cobra trophies - there are 30 bronze, 10 silver, 3 gold and 1 platinum.
G.I. JOE
Finish a level using only melee attacks on ground troops
Collect all File Cards
Collect all Intel Cards
Complete any mission in 2 player co-op
Complete mission with higher than 50% Dual Targeting kills
Achieve the worst rank on a level without going Man Down
Perform 10 barrel rolls in unison in any level in co-op
Collect and spend all 130 possible Battle Points
Purchase all G.I. JOE contacts
Collect all G.I. JOE Contacts
Complete every Mission on Hardcore Difficulty
Purchase all COBRA characters
Complete a Jungle or Tundra mission without going Man Down
Complete any mission using Baroness and Duke
Complete any mission using female characters only
Complete any Arctic, Desert, or Jungle mission using any COBRA character
Replay a mission and earn a higher score
Defeat every wave in all Satellite Strike mini-games
Complete all Sub-operation Missions
Complete any mission using Snake Eyes and Storm Shadow
Complete a mission using only Commando class characters
Destroy the M.A.S.S. Device
Complete all Jungle missions
Defeat Destro
Operate the turret in every vehicle in the game
Drive every G.I. JOE vehicle in the game
Defeat Storm Shadow in all three secret arenas
Collect 50% of all File Cards
Complete all Desert missions
Defeat Firefly
Gain access to a Commando Class Ability door
Complete all Arctic missions
Launch 50 enemies into the air and kill them.
Complete a mission using only Heavy class characters
Defeat Baroness
Complete a mission using only Combat class characters
Defeat every wave in one Satellite Strike mini-game
Purchase two G.I. JOE contacts
Gain access to a Combat Soldier Class Ability door
Gain the highest Mission Ranking
Activate the Accelerator Suit three times in any mission
Gain access to a Heavy Class Ability door
Pick up all three types of Point Multipliers in one mission