Here is the full list of all 12 Red Alert 3: Commander's Challenge trophies - there are 8 bronze, 3 silver and 1 gold.
Complete all 50 challenge missions under par time
Complete all 50 challenge missions
Complete all 13 main path challenge missions under par time
Complete all 13 main path challenge missions
Kill 20 Desolator Troopers
Complete any 25 challenge missions
Kill 20 Steel Ronin
Kill all giant bears in "Number One Threat to America"
Complete any 10 challenge missions
Kill 20 Enemy Commandoes
Complete the first challenge mission, "Dead Meat"
Complete all lessons in the tutorial