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.
Spot a mine which is later defused by another Engineer
Collect all Audio Logs
As a Medic, using the Transfer Supplies ability, give the last of your Supplies away
Win all storyline campaign missions (not including What-If missions) playing either Online Versus, or in Hard mode
Reveal an enemy in disguise
Take down an enemy with a Satchel Charge
While on offense, win the match in less than 30% of the time limit.
Win every Security campaign mission, including What-If missions
Reach Rank 5
Win all main missions of the Security campaign (not including What-If missions)
Win both story campaigns (not including What-If missions)
Take down an enemy with a Cortex Bomb
Attempt to Revive an objective-class teammate over a non-objective teammate near a Primary Objective
Complete all 3 Star Challenges
Complete all 1 Star Challenges
Complete your first 3 Star Challenge
Complete an Operative Primary Objective within 5 seconds of breaking disguise
Upgrade your team's command post
Disarm an HE charge
Complete your first 1 Star Challenge
Win every Resistance campaign mission, including What-If missions
Take down an enemy by shooting a grenade
While on defense, prevent the attackers from completing their first objective
Close an enemy team's shortcut
Use the last of your Supplies to refill a teammate's ammo rather than your own
Open a shortcut for your team
Detonate a HE Charge
Win all main missions of the Resistance campaign (not including What-If missions)
Complete an objective after first selecting it on the Objective Wheel
Reach Rank 2
While on defense, take down an attacker who's completing a Primary Objective
Take down an enemy with a mine
Capture an enemy's Command Post
Win any mission, whether campaign or What-If
Revive yourself
Take down an enemy with gunfire while knocked down
Win Founders' Tower as both factions in Campaign Mode
Win Labs as both factions in Campaign Mode
Kill an enemy with a Pyro Mine
Kill an enemy with a Napalm Grenade
Reach Level 24
Have a Field Regen Unit buff more than 3 players simultaneously
Kill an enemy with a UAV