There are 59 Trophies that can be collected.

Bronze

Short Out    
Defeat the Stalker in under 60 seconds    

Zookeeper    
Kill the Brawler in Haven without taking any damage    

Gardener    
Destroy 100 blast roots    

Slaybells    
Make Santa and his reindeer fly    

Bouncer    
Keep Chimeran forces from entering the Brewpub    

Calm Under Pressure    
Defeat the Brawler in the Post Office in under 2 minutes    

Snipe Hunt    
Collect all Deadeye rifles without dying while fighting the Widowmaker in St. Louis    

Roops!    
Knock a Hybrid off the cliffs in Mt. Pleasant, PA    

Frickin' Laser Beams    
Get to the first mineshaft without being hit by sniper fire in Mt. Pleasant, PA    

Vehicular Manslaughter    
Destroy 10 Warden vehicles while on the train    

Hello Driver    
Kill 5 drivers without destroying their vehicle    

BARF!    
Make 6 Wardens puke at the same time in the prison    

One Eyed Jack    
Find and kill 'Jack' in Graterford Prison    

No Escape    
Destroy all Warden vehicles in the Motorpool    

In This Together    
Defeat the Widowmaker in Times Square without killing a single Hybrid    

Good Fences    
Don't allow any counter-attackers into the Washington Square base    

Up Your Arsenal    
Get a kill with every weapon in your arsenal    

Overload    
Use the EMP to take down 10 Steelhead Auger shields    

Cheap Shots    
Kill 25 enemies firing the Auger through an object    

Grenadier    
Kill 3 or more Military Chimera with a single Grenade    

Raining Limbs    
Kill 25 Grims using only grenades    

Corpse Wagon    
Detonate fallen Leeches to kill 25 enemies    

Bloodborne    
Kill 3 enemies simultaneously using a single mutated body    

Grasshopper Unit    
Kill 5 Longlegs in mid-jump    

Sandman    
Kill 5 Grims in a row using only headshots    

Body Count    
Kill 1000 enemies    

Juggler    
Simultaneously burn, freeze and poison 4 separate enemies    

Nothing But Net    
Score a basket by lobbing a grenade through a basketball hoop    

Medusa    
Freeze 5 enemies at once and destroy them with a blast of the Cryogun's secondary fire    

Bull in a China Shop    
Freeze and melee kill 3 Ravagers    

Weaponsmith    
Upgrade 5 weapons in Campaign Mode    

This is my Rifle    
Fully upgrade one weapon in Campaign Mode    

Backstabber    
Kill 20 enemies with melee while they are idle    

Toast    
Use the upgraded Deadeye secondary fire to kill 2+ enemies, 5 times    

Counter-Sniper    
Use the Deadeye to kill 20 snipers    

Electric Avenue    
Use the EMP to take down 25 drones    

Warp Speed    
Use the Atomizer secondary fire to kill 30 enemies    

Feeling Lucky, Punk    
Detonate multiple Magnum rounds to kill 2+ enemies at once, 5 times    

Fireworks    
Use the Wildfire secondary fire to kill 6 enemies in one shot    

Boomstick    
Use the upgraded Rossmore secondary fire to set 6 enemies on fire at once    

Tag, You're It    
Kill 40 Bullseye tagged enemies    

Opportunity Knocks    
Kill 20 enemies with environmental objects    

Expert Sniper    
Get 50 headshot kills in Campaign Mode    

Collector    
Collect 10 journals    

Bookworm    
Collect 50% of the journals    

Waste Not    
Get 5 headshot kills with one Deadeye clip    

Shoe Leather    
Travel 30 km on foot    

Land, Sea, and Air    
Travel in 3 different vehicles on your journey    

Buckshot    
Kill 2+ enemies with one Rossmore blast    

Access Denied    
Absorb 1000 damage with Auger Shields    

From the Hip    
Kill 50 enemies with the Bullseye or Marksman while moving, without using zoom    

Chamber Full of Death    
Kill 5+ Hybrids at once by using the HE .44 Magnum secondary fire    

Helping Hands    
Revive a Co-op partner 20 times

Silver

Irresistible Force    
Complete Campaign Mode on any difficulty    

Master Mechanic    
Fully upgrade all weapons in Campaign Mode    

Archivalist    
Collect all journals    

Silent Partner    
Damage the same enemy in Cooperative Mode for 100 kills

Gold

Brutal    
Complete Campaign Mode on Superhuman

Platinum

Platinum Trophy    
Obtain all Gold, Silver, and Bronze Trophies for Resistance 3

http://www.ps3trophies.org/game/resistance-3/trophies/