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