Here is the full list of all 51 Battlefield: Bad Company trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
(Online) Achieve all the awards
(Online) Glide in the parachute for 3 seconds
(Online) Reach Rank 25
(Online) Collect 50 unique dog tags
(Online) Achieve half of all awards
(Online) Reach Rank 20
(Online) 100 kills using vehicle
(Online) Play 100 online matches
(Online) Get at least one kill in every vehicle
(Online) Place #1 in a ranked match
(Online) Have 20 Squad members spawn on you without dying in a single round
(Online) Use Squad in the menu, find a friend and play one round
(Online) Destroy 1000 walls
(Online) Reach Rank 8
(Online) Collect 5 unique dog tags
(Online) Knock down 1000 trees
(Online) Reach Rank 3
Kill 25 enemies
(Online) Participate in one online match (Ranked)
(Online) Take 3 pictures using the image system
Battlefield: Bad Company
Complete 'Welcome To Bad Company' on normal
Complete 'Welcome To Bad Company' on hard
Complete 'Acta Non Verba' on normal
Complete 'Acta Non Verba' on hard
Complete 'Crossing Over' on normal
Complete 'Crossing Over' on hard
Complete 'Par for the Course' on normal
Complete 'Par for the Course' on hard
Complete 'Air Force One' on normal
Complete 'Air Force One' on hard
Complete 'Crash and Grab' on normal
Complete 'Crash and Grab' on hard
Find 5 unique collectables
Find half of all collectables
Complete one mission without dying (any difficulty)
Complete 'Ghost Town' on normal
Complete 'Ghost Town' on hard
Kill 25 enemies in a helicopter
Destroy 200 walls
Use Auto Injector 50 Times
Knock down a small forest
Destroy 50 vehicles. (containing enemy AI)
Drive all vehicle types (Jeep, Tank, Heli, Boat)
Hit hostile helicopter with laser designator
Find all collectables
Find one gold bar
Find half of the gold bars
Find all gold bars
Climb to the highest spot in the game
(Online) Get 10002 kills