Here is the full list of all 51 Need for Speed: Undercover trophies - there are 46 bronze, 1 silver, 3 gold and 1 platinum.
Platinum Trophy
Finish 119 Multiplayer Races in any position
Won 25 Ranked Multiplayer events
Win a Ranked Multiplayer event against 7 human players
Win a Ranked Multiplayer Cops N' Robbers event
Won a Multiplayer Ranked Game
Infected with the Cops N' Robbers virus by another player in a Cops and Robbers event.
Participated in any Community Day. Visit NeedforSpeed.com for more info.
Dominate the Tri-City Run event
Dominate the North River Expressway event
Dominate the East I-5 event
Dominate 100% of Career by beating all the track records.
Win all the Highway Battles in Career
Avoid 12 Spike Strips total in Career pursuits
Sucessfully complete 50 Pursuits
Dominate the Pine Creek & Douglas event
Dominate the South Canyon Hwy event
Take a Photo and upload it to NeedforSpeed.com
Create or use an existing account to sign into EA Nation
Dominate the East Fasulo Bridge event
Finish the Career Story
Takeout all the 'Goons' in Career
Complete the mission 'Double Trouble'
Avoid 50 Road Blocks in Career
Complete the Nickel sequence in mission 'Payback'
Avoid a spike strip in a Pursuit and successfully evade in Career
Get $100,000 Cost to State in a single pursuit and evade
Avoid 5 Road Blocks in a Pursuit and successfully evade in Career
Disable 10 Police Cars in a Pursuit and successfully evade in Career
Purchase or win any 5 cars for your garage.
Discovered all 3 Pro Shops in Career
Dominate the Bay Drive & Harbor event
Face off against Rose in 'Rollercoaster'
Complete all Hot Car Missions
Unlock Port Crescent in Career
Discovered all 3 Tuning Shops in Career
Escape from a helicopter in a succesfully completed pursuit. (Must be Career level 8 or greater)
Face off against Nickel in 'Road Rage'
Disable 100 Police vehicles.
Dominate 25 events in Career
Dominate the Gold Coast to Ocean event
Complete the Carmen sequence in the mission 'Rematch'
Complete the Hector sequence in the mission 'Kingpin'
Unlock Sunset Hills in Career
Complete the Zack sequence in 'The Trap' mission.
Face off against Hector in 'Versus'
Sucessfully complete 5 Pursuits
Face off against Carmen in 'The Game'
Face off against Zack in 'Rush Hour'
Customize a car in Career mode.
Acquire your first car in Career Mode