Successfully complete one of the following tasks to get a trophy:

Prologue (Bronze): Complete Prologue.
Crash Site (Bronze): Complete Crash Site.
The Village (Bronze): Complete The Village.
Spare Parts (Bronze): Complete Spare Parts.
Village Attack (Bronze): Complete Village Attack.
Prophesized One (Bronze): Complete Prophesized One.
The Survivors (Bronze): Complete The Survivors.
Prison Escape (Bronze): Complete Prison Escape.
Defending the Ark (Bronze): Complete Defending the Ark.
The Collector (Bronze): Complete The Collector.
The Revolt (Bronze): Complete The Revolt.
Dear Diary (Bronze): Dear Diary - Found a journal.
Tesla's Apprentice (Bronze): Tesla's Apprentice - Upgraded first weapon.
Grand Theft...UFO? (Bronze): Grand Theft...UFO? - Hijacked 20 UFOs.
Blind Luck (Bronze): Blind Luck - Kill one of each enemy footsoldier using blind fire.
Captain of the Ship (Bronze): Captain of the Ship - Destroy 10 enemy aircraft while yours is on fire.
Forgot My Two Cable (Bronze): Forgot My Tow Cable - Fly though an Archon's legs.
Fireworks (Bronze): Fireworks - Kill 10 enemies by exploding a piece of dynamite in the air.
Get Your Feet Wet (Bronze): Get Your Feet Wet - Buzz the water.
99 Red Balloons (Bronze): 99 Red Balloons - Kill 10 enemies while they are in anti-gravity bubble.
Cliffhanger Killer (Bronze): Cliffhanger Killer - Kill 50 enemies while in vertical cover.
Death from Above (Bronze): Death from Above - Kill 50 enemies while in hover.
Bird of Prey (Bronze): Bird of Prey - Kill 25 ground enemies using your rocket pack guns.
Mark of the Adept (Bronze): Mark of the Adept - Kill 5 UFOs in the Prologue.
Rocket Clothesline (Bronze): Rocket Clothesline - Perform a melee right after turning off rocket pack thrusters.
Terminal Velocity (Bronze): Terminal Velocity - Free fall for 10 seconds.
The Squishy Center (Bronze): The Squishy Center - Kill a Sarpa piloting an Archon.
Cleanup on Aisle Three (Bronze): Cleanup on Aisle Three - Kill 100 enemies with headshots.
Rochambeau, I Go First (Bronze): Rochambeau, I Go First - Kill 50 enemies with melee attacks.
Blue Light Special (Bronze): Blue Light Special - Kill 3 enemies with one grenade.
Killing Spree (Bronze): Killing Spree - Kill 10 enemies within 60 seconds.
Those Aren't Fortune Cookies (Bronze): Those Aren't Fortune Cookies - Step on 10 slugs.
Master of Arms (Bronze): Master of Arms - Kill an enemy with every weapon.
I'm a Rocketman, Baby (Bronze): I'm a Rocketman, Baby - Perform 100 special maneuvers while using the rocket pack.
Float Like a Butterfly (Bronze): Float Like a Butterfly - Kill 10 attackers immediately after escaping from their melee.
Into the Void (Silver): Complete Into the Void.
Breaking Camp (Silver): Complete Breaking Camp.
Tower of Return (Silver): Complete Tower of Return.
Bookworm (Silver): Bookworm - Found all journals.
Grease Monkey (Silver): Grease Monkey - Upgraded all weapons.
Pack Rat (Silver): Pack Rat - Acquired all 30,000 tech points.
Demolition Derby (Silver): Demolition Derby - Collide with another UFO 10 times.
The Big Bang (Silver): The Big Bang - Destroy a Knight using a grenade.
Light up the Sky (Silver): Light Up the Sky - Destroy 25 targets with the Ark's AA guns.
The Devastator (Silver): The Devastator - Destroy 25 UFOs while pilting a Survivor fighter.
Dark Void (Gold): Complete Dark Void.
Ultimate Bad Ass (Gold): Ultimate Bad Ass - Complete Dark Void on Hardcore.
Dark Void 100% Complete (Platinum): Earn all trophies.