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.
Revive yourself
Win any mission, whether campaign or What-If
Complete an objective after first selecting it on the Objective Wheel
Capture an enemy's Command Post
Take down an enemy with gunfire while knocked down
Take down an enemy by shooting a grenade
While on defense, prevent the attackers from completing their first objective
Complete your first 1 Star Challenge
Reach Rank 2
Win all main missions of the Security campaign (not including What-If missions)
Win all main missions of the Resistance campaign (not including What-If missions)
Win both story campaigns (not including What-If missions)
Win every Resistance campaign mission, including What-If missions
Win every Security campaign mission, including What-If missions
Win all storyline campaign missions (not including What-If missions) playing either Online Versus, or in Hard mode
Open a shortcut for your team
Close an enemy team's shortcut
While on defense, take down an attacker who's completing a Primary Objective
Reveal an enemy in disguise
While on offense, win the match in less than 30% of the time limit.
Disarm an HE charge
Take down an enemy with a mine
Upgrade your team's command post
Attempt to Revive an objective-class teammate over a non-objective teammate near a Primary Objective
As a Medic, using the Transfer Supplies ability, give the last of your Supplies away
Spot a mine which is later defused by another Engineer
Complete an Operative Primary Objective within 5 seconds of breaking disguise
Take down an enemy with a Cortex Bomb
Detonate a HE Charge
Use the last of your Supplies to refill a teammate's ammo rather than your own
Take down an enemy with a Satchel Charge
Complete your first 3 Star Challenge
Complete all 1 Star Challenges
Complete all 3 Star Challenges
Collect all Audio Logs
Reach Rank 5
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