Here is the full list of all 20 Modern Combat: Domination trophies - there are 19 bronze and 1 silver.
Reach Level 72
Get 500 kill assists (any game types)
Reach Level 40
Kill 4 enemies with a frag grenade thrown with the grenade launcher
Eliminate 300 enemies only with sniper rifles (any game types)
Eliminate 1000 enemies (any game types)
Win one match of each game type in every map
Successfully knife 50 enemies (any game types)
Make 100 head shots (any game types)
Head shot an objective carrier 10 times
Perform at least one killing spree on all maps
Perform a multi-kill with a grenade 3 times (any game types)
As the Team Leader, escape 10 times
Capture a total of 150 territories in Domination
Capture a total of 100 territories in Domination
Reach Level 7
Take over a CPU and kill your assassin 10 times (offline only)
Defuse a bomb or deactivate a missile 10 times
Eliminate 100 enemies (any game types)
Win a match (any game types)