Successfully complete one of the following tasks to get a trophy:
Rampage! (Bronze): Kill 40 hybrids in the Single Player Campaign.
Covert Ops (Bronze): Collect 5 pieces of Intel in the Single Player Campaign.
Nowhere to Hide (Bronze): Tag and kill 30 enemies with the Bullseye in the Single Player Campaign.
Sharpshooter (Bronze): Get 30 headshots while scoped in with the Fareye or Marksman in the Single Player Campaign.
Explosives Expert (Bronze): Get 150 kills with the Carbine 40mm, LAARK, or Frag Grenade in the Single Player Campaign.
They Go "Boom" (Bronze): Get 30 kills with the Magnum secondary fire in the Single Player Campaign.
Pyromaniac (Bronze): Set 100 enemies of fire with the Bellock Semi-Automic, Air-Fuel Grenade, Spider Grenade, or environmental hazard in the Single Player Campaign.
Spitting Lead (Bronze): Kill 50 enemies using the Wraith with the force barrier engaged in the Single Player Campaign.
I See You (Bronze): Kill 50 enemies through solid matter with the Auger in the Single Player Campaign.
Talk To The Hand (Bronze): Use the Auger force barrier to stop 150 incoming enemy shots in the single player Campaign.
For Close Encounters (Bronze): Get 10 one-hit head-shot kills with the Shotgun in the Single Player Campaign.
Pincushion (Bronze): Get 50 kills with the Hedgehog in the Single Player Campaign.
Up Close and Personal (Bronze): Get 50 melee kills with any weapon in the Single Player Campaign.
Wrecking Machine (Bronze): Destroy 40 vehicles in the Single Player Campaign.
Mind Your Surroundings (Bronze): Get 50 indirect kills using explosive objects in levels in the Single Player Campaign.
Berserker (Bronze): Use every berserk at least once in Online Competitive Multiplayer.
Specter Recon (Bronze): Collect 50 pieces of gray tech in the Cooperative Campaign.
Specter Initiate (Bronze): Complete 20 missions in the Cooperative Campaign.
Team Player (Bronze): Complete 5 missions with a full party of 8 in the Cooperative Campaign.
Tour of Duty (Bronze): Complete one mission on each region in the Cooperative Campaign.
Salute Me (Silver): Achieve the rank of Lieutenant.
Exotic Weapon Collector (Silver): Get 20 kills with each weapon in the Single Player Campaign.
Master Spy (Silver): Collect all the Intel documents in the Single Player Campaign.
Snipe Hunt (Silver): Kill 30 Spinners in the Single Player Campaign.
Xenocide (Silver): Kill 1000 enemies in the Single Player Campaign.
Point Man (Silver): Earn 1 million XP from ranked games in online Competitive mode.
Specter Officer (Silver): Reach max level (30) with one class in the Cooperative Campaign.
Primarch Hunter (Silver): Kill 200 Elite Chimerans in the Cooperative Campaign.
Killing Machine (Gold): Score 10,000 kills in ranked matches in Online Competitive Multiplayer.
Specter Intel (Gold): Collect all Intel in the Cooperative Campaign.

Additionally, there are nine secret trophies:
Recycler (Bronze): Defeat the Goliath in the Single Player Campaign.
Fried Calamari (Bronze): Defeat the Kraken in the Single Player Campaign.
Exterminator (Bronze): Defeat the Mother Spinner in the Single Player Campaign.
Flyswatter (Bronze): Defeat the Swarm in the Single Player Campaign.
The Bigger They Are (Bronze): Defeat the Leviathan in the Single Player Campaign.
Big Game Hunter (Bronze): Defeat the Marauder in the Single Player Campaign.
R.I.P. Jordan Shepherd (Bronze): Defeat Daedalus, Complete the Single Player Campaign.
OMGWTFBBQ (Bronze): Complete the Single Player Campaign on Superhuman.
Platinum Trophy (Platinum): Obtain all Gold, Silver, and Bronze Trophies for Resistance 2.