Here is the full list of all 21 History Legends of War: Patton (EU) trophies - there are 6 bronze, 6 silver, 8 gold and 1 platinum.
Complete all trophies
Complete the Third Army (Campaign Mode)
Kill 15 German soldiers with knife (Campaign Mode)
Complete the game (Campaign Mode)
Complete fourth operation without casualties (Campaign Mode)
Make first upgrade (Campaign Mode)
Unlock all types of units (Campaign Mode)
Complete third operation (Campaign Mode)
Get 10 heroic victories (Campaign Mode)
Destroy 200 German units (Campaign Mode)
Complete second operation (Campaign Mode)
Destroy 100 German units (Campaign Mode)
Recruit first aircraft (Campaign Mode)
Get 5 heroic victories (Campaign Mode)
Complete first operation (Campaign Mode)
Recruit first bazooka (Campaign Mode)
Destroy 50 German units (Campaign Mode)
Recruit first tank (Campaign Mode)
Max out any of Patton's Skills (Campaign Mode)
Complete first mission (Campaign Mode)
Complete tutorial