There are 27 Trophies that can be collected.

Bronze

Rule #1    
Complete first co-op activity

Nice goin' Abs.    
Complete first fingerprint lifting

Rule #8    
Complete first interview

Like shooting fish in a pond    
Complete first safe cracking

You know I'm awesome    
Collect first piece of evidence

Silver

Hey, I'm a hacker.    
Complete first database search

Abigail Sciuto FTW    
Complete first fingerprint comparison     

Abbycadabra    
Complete first chemical analysis     

Rule #39    
Complete first ballistics test     

Cooking up some awesome    
Complete first footprint comparison     

Rule #38    
Complete first deduction     

Waddaya got for me, Duck    
Complete first autopsy

Rule #3    
Complete first interrogation

Atlantic City    
Complete first crime scene     

Dirty Harry    
Complete second crime scene     

Bank Heist    
Complete third crime scene     

BBQ'd Apartment     
Complete fourth crime scene     

Front Lines    
Complete fifth crime scene     

Torture Chamber    
Complete sixth crime scene     

Five Star Accommodations    
Complete seventh crime scene     

NCIS 1, Terrorists 0    
Save the world from terrorists

Gold

McGPS    
Complete first satellite tracking

Probie Wan Kenobie    
Complete Episode 1     

NCIS Investigator    
Complete Episode 2     

NCIS Agent    
Complete Episode 3     

Very Special Agent    
Complete Episode 4

Platinum

Justice has been served.    
Unlock All Trophies 

http://www.ps3trophies.org/game/ncis/trophies/