There are 50 Trophies that can be collected.

Bronze

All Members    
Add each teammate to the party at least once.     

Jumper    
Get onto the Grand Lancer's head.     

Spider Killer    
Destroy all of the Spider's legs.     

Hacker    
Destroy all enemies with the mobile gun battery.     

Jackpot    
Hit the jackpot on a vending machine.     

Transport Takedown    
Destroy the Iron Whale's four engines.     

Smash Master    
Get 50 smash bonuses in Campaign.     

Multi-Kill Master    
Get 50 multi-kill bonuses in Campaign.     

Headshot Master    
Get 50 headshot bonuses in Campaign.     

One-Shot Master    
Get 50 one-shot bonuses in Campaign.     

Lifesaver    
Use first-aid kits to revive teammates 10 times.     

A Friend Indeed    
Purchase nanomachines for a teammate.     

Shop Master    
Access all shopping terminals.     

Spendthrift    
Spend 10,000 credits at vending machines.     

Assault Shooter Killer    
Destroy 100 Assault Shooters in Campaign.     

Tactician    
Get enemies to kill each other 50 times.     

Weapon Crafter    
Upgrade a weapon.     

Craftsman    
Fully upgrade one weapon category.     

Data Collector    
Collect 20 SECURITY-COM in Campaign.

First Victory    
Win an online vs. match with any rule set.     

Still Alive    
Clear a stage in INVASION mode.     

Resistance Hero    
Clear all stages in INVASION mode.     

Battlemaster    
Win an online vs. match with all rule sets.

Silver

Data Retrieval Complete    
Collect all SECURITY-COM in Campaign.     

Skill Master    
Get all nanomachines within 1 playthrough in Campaign.     

Rust Crew    
Clear all chapters on SURVIVOR Mode.

Veteran Soldier    
Reach online level 50.

Gold

Challenge Master    
Clear all online mode challenges.

Platinum

Platinum Trophy    
Earn all other trophies in the game.

21 Secret

http://www.ps3trophies.org/game/binary-domain/trophies/