There are 20 Trophies that can be collected.

Bronze

Specialist
Reach Level 7

Sergeant Major of the Army
Reach Level 40

Master of Mass Destruction
Win one match of each game type in every map

Raining Shrapnel
Kill 4 enemies with a frag grenade thrown with the grenade launcher

Billy the Kid
Make 100 head shots (any game type)

Alexander the Great
Capture a total of 100 territories in Domination

Welcome to the Family
Win a match (any game types)

The Ghost Avenger
Take over a CPU and kill your assassin 10 times (offline only)

Insane Sharpshooter
Eliminate 300 enemies only with sniper rifles (any game types)

Heavy Counter
Perform a multi-kill with a grenade 3 times (any game types)

Legendary Gunslinger
Perform at least one killing spree on all maps

Team Savior
As the Team Leader, escape 10 times

Ultimate Team Player
Get 500 kill assists (any game types)

Stop Poking Me!
Successfully knife 50 enemies (any game types)

War Veteran
Eliminate 100 enemies (any game types)

Death Bringer
Eliminate 1000 enemies (any game types)

Dominating
Capture a total of 150 territories in Domination

Priceless
Head shot an objective carrier 10 times

Hope Buster
Defuse a bomb or deactivate a missile 10 times

Silver

Supreme Commander
Reach Level 72

http://www.ps3trophies.org/game/modern-combat-domination/trophies/