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