Here is the full list of all 39 Men In Black: Alien Crisis trophies - there are 26 bronze, 7 silver, 5 gold and 1 platinum.
Unlock all trophies in game
Defeat Adorian Elite Guard in Story Mode
Dodge the mines placed by Nethera in Story Mode
Defeat 40 bikers in Story Mode
Defeat 70 bikers in Story Mode
Destroy 3 enemy platforms in Story Mode
Achieve a 25x multiplier in a Story Mode
Neuralize 7 humans in Story Mode
Escape Serleena’s drag attack
Successfully finish the Virtual Reality training program in Story Mode
Crash Chauncey’s party in Story Mode
Defeat Nakkadan Elite Guard in Story Mode
Scan 2 hidden aliens in Story Mode
Defeat enemies using 10 different combos
Don't be detected while flying the car
Start playing in Story Mode
Achieve at least 150,000 points in one V.R. Mission
Achieve at least 200,000 points in one V.R. Mission
Achieve at least 300,000 points in one V.R. Mission
Complete all the Competitive maps in V.R. Missions
Defeat 50 enemies with the Std. Issue 1995
Defeat 60 enemies with the Noisy Cricket
Defeat 250 enemies with the Tribarrel
Defeat 350 enemies with the Tribarrel
Defeat 100 enemies with the Adorian Crossbow
Defeat 200 enemies with the BANGer
Freeze 30 enemies with the Icer
Use the Anti-Gravity grenade on 30 enemies
Use the Refracto Shield to reflect 100 enemy projectiles
Defeat 20 enemies with the Rocket Launcher while flying the car
Defeat 30 enemies while they're under the effect of Cerebro Accelerator
Defeat 700 enemies
Defeat Khnemu in Story Mode
Complete Story Mode as an Agent
Gather 50 upgrade points
Defeat 900 enemies
Defeat Nethera and save Catyana
Complete Story Mode as an Elite Agent
Complete all the missions in Story Mode