There are 47 Trophies that can be collected.

BRONZE

Got to Smash Them All
Smash every Billboard

The Gatecrasher
Break through every Security Gate

Love Them and Leave Them
Drive every Car

Networking
Find every Jack Spot

Cameraman
Trigger every Speed Camera

Go Pro or Go Home
Unlock all the Pro mods on a car (Single Player)

Feeling the Need
Empty a full nitrous bar without hitting anything

Fix Me Up
Use a Bodyshop to paint or repair your car for the first time

Switcheroo
Use a Jack Spot in a Pursuit (Single Player)

Kitchen Sink
Use a Billboard and a Jack Spot to successfully evade a pursuit (Single Player)

Social Climber
Get 5 or more NFS friends

How Do You Like Me Now?
Beat a friend’s Autolog Recommendation

Moving On Up
Move up the Most Wanted List for the first time

Nothing Personal
Takedown a friend in Multiplayer

After Market
Unlock a mod for a car in Multiplayer

Mix Master
Play a Custom Speedlist you have created (Multiplayer)

In Your Face
Smash a friend’s face on a billboard and beat their jump distance

Pit Stop
Repair a burst tire at a Bodyshop

Alpha Dog
Shut down Most Wanted car number 10: Alfa Romeo 4C Concept (Single Player)

Charming
Shut down Most Wanted car number 9: Shelby COBRA 427® (Single Player)

Blackout
Shut down Most Wanted car number 8: Mercedes-Benz SL 65 AMG (Single Player)

Lexus Ranger
Shut down Most Wanted car number 7: Lexus LFA (Single Player)

Track Weapon
Shut down Most Wanted car number 6: McLaren MP4-12C (Single Player)

Arachnophobic
Shut down Most Wanted car number 5: Porsche 918 Spyder Concept (Single Player)

Main Avent
Shut down Most Wanted car number 4: Lamborghini Aventador (Single Player)

White Gold
Shut down Most Wanted car number 3: Bugatti Veyron Super Sport (Single Player)

Mighty Wind
Shut down Most Wanted car number 2: Pagani Huayra (Single Player)

Gotcha
Get Busted for the first time

First Strike
Takedown your first Cop

Slip the Cuffs
Drive through a roadblock without hitting it

Battering Ram
Smash through a roadblock without crashing

Sidewinder
Do a 250 yard (228.6 meter) drift

Iron Boots
Drive over 5 spike strips with re-inflates equipped

Escape Velocity
Jump over 200 yards (182.88 meters) through a Billboard

Fast Forward
Trigger a speed camera at over 200mph (321.97km/h)

SILVER

The Heat is Off
Escape successfully from all Heat levels

Licensed to ill
Customize your license plate and number in Multiplayer

The Modfather
Unlock 3 Pro Mods in Multiplayer

Rim Shot
Escape the cops with at least one blown tire

Don’t Blink
Shut down Most Wanted car number 1: Koenigsegg Agera R (Single Player)

Troublemaker
Takedown 50 Cops

Mauled
Wreck 10 cops in a single pursuit in the Ford F-150 SVT Raptor

Beast from the East
Escape from the cops in the Marussia B2

Gladiator
Takedown every racer at least once in a single race

GOLD

Most Wanted Rides
Own all the Most Wanted cars (Single Player)

Second is Nothing
Finish first in every race, in every car (Single Player)

PLATINUM

None More Wanted
Awarded for successfully collecting all Most Wanted trophies

http://www.ps3trophies.org/game/need-for-speed-most-wanted-vita/trophies/