Here is the full list of all 43 Brink achievements.
The base game contains 36 achievements, and there is 1 DLC pack containing 7 achievements.
Win Labs as both factions in Campaign Mode
Win Founders' Tower as both factions in Campaign Mode
Kill an enemy with a Napalm Grenade
Kill an enemy with a Pyro Mine
Kill an enemy with a UAV
Have a Field Regen Unit buff more than 3 players simultaneously
Reach Level 24