There are 20 Trophies that can be collected.

Bronze

Hat Trick    
Win three Autolog Challenges in a row against the same Friend    

Fighting Back    
Take on an Autolog 'Beat You' Recommendation and beat your Friend's score    

Maximum Carnage!    
Trigger a Super Feature with 100% power    

Chain Reaction    
Get a 7x Explosion Chain or better    

The Big Bang    
Get a 25x Explosion Combo or better    

Trail of Destruction    
Get a 15x Smash Chain or better    

Longshot    
Make a Punt Skillshot of 50 yards or more    

Scattershot    
Make 5 or more Skillshots with one Crashbreaker    

Expensive Taste    
In any Road Trip, blow up all three Sports Cars and the Gold Car and finish the event    

Maximum Withdrawal    
Collect $9,000,000 from a single Bank Truck    

Did You Let One Go?    
Let a Gas Tanker escape without exploding    

Blast Zone    
Damage 20 vehicles or more with a single Crashbreaker    

Pure Gold    
Earn $30,000,000 from a Gold Car in one event    

Blind Luck    
Survive the Fog in a Road Trip with no escapes… but without using your Crashbreaker    

Set ‘Em Up, Knock ‘Em Down    
Score $30,000,000 or more in any Pile Up, but without firing your Crashbreaker more than twice    

Button Masher!    
Fire your Crashbreaker 30 times or more in a single Rush Hour    

Damage Limitation    
In any Pile Up, get to Inferno with a x5 multiplier… but without blowing up a single vehicle    

That Sinking Feeling    
Jump down all three holes on Blueclaw& 1st in Road Trip, without failing the event    

Razed to the Ground!    
Destroy all the buildings in a junction in any single event (Super Feature doesn’t count!)

Silver

Burnout Crash All-Star    
Collect all 270 Stars

http://www.ps3trophies.org/game/burnout-crash/trophies/