Here is the full list of all 51 R.U.S.E. trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Destroy 5000 enemy units
Use all RUSEs
Recover Germany's secret weapon plans
Survive to see the German capitulation
Capture 50 buildings
Successfully hold Bastogne
Complete Operation Market Garden
Get to level 20
Complete 50% of the secondary objectives from the Campaign.
Complete the Cotentin Campaign
Successfully land at Utah Beach
Complete the Italian Campaign
Eliminate the last Italian forces
Neutralize the Italian secondary HQ by moving from cover to cover
Play two RUSEs on the same sector
Throw the Axis out of Africa
Successfully hold Kasserine Pass
Seize Colditz Castle
Complete all trophies
Prevent the Russians from attacking the western allies
Prevent World War III in Easy difficulty level
Prevent World War III in Medium difficulty level
Prevent World War III in Hard difficulty level
Complete all the secondary objectives from the Campaign.
Complete an operation
Complete all operations' bonus objectives
Complete all cooperative operations
Complete all 1 vs. all operations
Complete all 1 vs. 1 operations
Complete all operations
Defeat an A.I. in battle mode
Defeat an A.I. in battle mode on Medium difficulty level and in all time periods (39/42/45)
Defeat an A.I. In battle mode on Hard difficulty level with Total victory
Defeat an A.I. in battle mode while playing each nation
Defeat all A.I. profiles in 1v1 battle at least in Medium difficulty
Reach the Veteran league.
Reach the Elite league.
Get to level 100
Defeat one of Eugen Systems' team or someone having already unlocked this trophy
Play a four-player game with your friends only
Play a game on every map in a ranked match
Play a game with a friend in the same team
Play a game with a stranger in team ranked match
Achieve a victory in every ranked match mode
Defeat an opponent without using the airfield and armor and artillery base camps in a ranked match
Defeat an opponent with air units only in a ranked match
Achieve a 90% or more survival ratio in a ranked match
Achieve a 200% or more kill rate in a ranked match
Win 5 games with every nation in ranked matches
Achieve a winning streak of 3 in ranked matches
Achieve a winning streak of 10 in ranked matches