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.
Take down an enemy by shooting a grenade
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
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
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 all 3 Star Challenges
Collect all Audio Logs
Reach Rank 5
Open a shortcut for your team
Close an enemy team's shortcut
Win any mission, whether campaign or What-If
Reveal an enemy in disguise
Take down an enemy with gunfire while knocked down
Complete all 1 Star Challenges
Attempt to Revive an objective-class teammate over a non-objective teammate near a Primary Objective
While on defense, prevent the attackers from completing their first objective
Capture an enemy's Command Post
While on defense, take down an attacker who's completing a Primary Objective
Complete an objective after first selecting it on the Objective Wheel
Revive yourself
Reach Rank 2
Complete your first 3 Star Challenge
Complete your first 1 Star Challenge
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