Here is the full list of all 37 Brink (JP) trophies - there are 14 bronze, 19 silver, 3 gold and 1 platinum.
Earn all other trophies
Win every Resistance campaign mission, including What-If missions
Collect all Audio Logs
Take down an enemy with a Satchel Charge
Reach Rank 5
While on offense, win the match in less than 30% of the time limit.
Take down an enemy with a Cortex Bomb
Upgrade your team's Command Post
Complete all 3 Star Challenges
Complete all 1 Star Challenges
Complete an Operative Primary Objective within 5 seconds of breaking disguise
Spot a mine which is later defused by another Engineer
Reveal an enemy in disguise
Disarm an HE charge
Close an enemy team's shortcut
Win every Security campaign mission, including What-If missions
As a Medic, using the Transfer Supplies ability, give the last of your Supplies away
Take down an enemy by shooting a grenade
Win all storyline campaign missions (not including What-If missions) playing either Online Versus, or in Hard mode
Win both story campaigns (not including What-If missions)
Win all main missions of the Resistance campaign (not including What-If missions)
Complete your first 3 Star Challenge
Complete your first 1 Star Challenge
While on defense, take down an attacker who's completing a Primary Objective
Take down an enemy with a mine
While on defense, prevent the attackers from completing their first objective
Win all main missions of the Security campaign (not including What-If missions)
Reach Rank 2
Attempt to Revive an objective-class teammate over a non-objective teammate near a Primary Objective
Detonate a HE Charge
Capture an enemy's Command Post
Open a shortcut for your team
Take down an enemy with gunfire while knocked down
Complete an objective after first selecting it on the Objective Wheel
Win any mission, whether campaign or What-If
Use the last of your Supplies to refill a teammate's ammo rather than your own
Revive yourself