There are 50 Trophies that can be collected.

Bronze

SMASHING    
Drive through 100 breakable objects in a single event.    

WORLD's BEST BACKWARDS DRIVER    
Drive backwards for a total of 60 seconds in a single event.

SHOCK VALUE    
Use 15 turbos in a single event    

READY, SET, GO!    
Get a perfect Quick Start    

HOP-A-LONG    
Hop 20 times in a single event.    

ALL MINE!    
Earn 30 seconds of bonus time by destroying Lemons in a single Attack mode event.    

DANGEROUS CARGO    
Destroy 5 explosive trucks in a single Attack Mission.

SURVIVOR    
Get a gold trophy in a single Survivor Mission.    

DROP THE BOMB    
Knock the Disruptor out of any opponent's grasp 5 times in a single Disruptor Challenge.    

EYE IN THE SKY    
Destroy 3 Lemons with the Satellite Quake weapon in a single Hunter Mission.    

POWER SURGE    
Collect 3 bonus batteries in a single Survival Mission.

ROAD RAGE    
Bash 15 Lemons in Hunter Mode.    

JET SETTER    
Jump over an airplane's wings 3 times in Airport Arena.    

JAM YOUR GEARS    
Drive through 10 fruit stands in Italy Arena.

BUSHWACKED!    
Drive through 6 hedge sculptures in the Castle Courtyard in Hyde Tour.    

LIGHTS OUT    
Drive through 15 lamp posts in London Arena.    

SHARE THE SPOTLIGHT    
Grab the attention of the Trimaran spotlight 3 times in a single event.

TRACTOR TRIPPER    
Tip 3 tractors in a single Canyon Run, Timberline Sprint event or Radiator Springs Arena.    

HUDSON HORNET    
Drift on a drift strip for a continuous 6 seconds in a single event.    

TOKYO VANDAL    
Drive through 17 street signs in a single Tokyo race.    

RUNAWAY PANCAKE    
Collide 3 times with a landing aircraft in Runway Tour.    

TRICK MASTER    
String together 5 tricks in a single jump.    

BASH 'N' CRASH    
Side bash 100 cars.

TAILGATER    
Spend 5 minutes drafting cars.

STUNT DRIVER    
Perform 150 air tricks.    

TURBO CHARGED    
Use turbo 250 times.    

EAT MY DUST    
Get 40 perfect Quick Starts.    

AGENT – FOURTH CLASS    
Unlock any 10 badges or crests.    

AGENT – THIRD CLASS    
Unlock any 20 badges or crests.

LOCK 'N' LOAD    
Collect and use each type of weapon.    

LICENSE EXPIRED!    
Destroy 250 Lemons in Attack Mode.    

DEAD EYE    
Hit the chase car 25 times with any weapon in Survival Mode.    

SPECIAL DELIVERY    
Deliver the Disruptor 35 times in Disruptor Mode.    

DISRUPTOR INTERRUPTOR    
Knock the disruptor out of 30 opponents' grasps in Disruptor Mode.    

ROAD TRIP    
Drive 250 kilometers.    

BUMPER CAR    
Take out 50 opponents in Arena Mode.

FREQUENT FLYER    
Spend 20 minutes in the air.

Silver

NOTHING BUT AIR TRICKS    
Complete 10 air tricks in a single event.

CAPITOL VIEW    
Gain access to the upper level of a skyscraper in Tokyo Arena.

MAKE THEM QUAKE    
Hit any opponent 2 times with the Satellite Quake weapon.

ISLAND HOPPER    
Use the island as a shortcut in Casino Tour.

DISRUPTOR DISRUPTOR    
In Disruptor Mode, destroy the opponent's base.

BULLDOZER IN A CHINA SHOP    
Drive through 500 breakables.

IN YOUR FACE    
Drive backwards for 15 minutes.

AGENT – SECOND CLASS    
Unlock any 30 badges or crests.    

AGENT – FIRST CLASS    
Unlock any 40 badges or crests.

INTERNATIONAL CAR OF MYSTERY    
Get a bronze trophy or better in every C.H.R.O.M.E. mission.

Gold

LEADER OF THE TRACK    
Get a gold trophy in all of the C.H.R.O.M.E. Hunter Missions.

MASTER TRACKER    
Collect 20 Spy Point Pick-ups.

Platinum

MASTER AGENT    
Unlock 49 badges and crests.

http://www.ps3trophies.org/game/cars-2-the-video-game/trophies/