Bronze

Welcome to Planet 51
Complete the tutorials.

Breaking News!
Complete level 10 in the task "Glipforg News Paperboy".

Lawnmower Master
Complete level 10 in the task "Lawnmower Boy".

Glipforg Deliveries
Complete level 10 in the task "Glipforg Deliveries".

The Dog Catcher
Complete level 10 in the task "Too Many Dogs in this Town".

Born to Park
Complete level 10 in the task "Parking Boy".

Glipforg Taxi Driver
Complete level 10 in the task "Taxi!".

Circus Cleaner
Complete level 10 in the task "World's cleanest circus".

Pro Cyclist
Travel 12 miles by bicycle.

Pro Driver
Travel 300 miles by car.

Reckless Driver
Destroy 30 pieces of property in 60 seconds.

Fugitive
Elude the law enforcers 3 times in a row in the same vehicle outside of a mission.

Alien!
Achieve and maintain the maximum level of alert for 3 minutes outside of a mission.

Perfect Gardener
Complete the mission "Neera's Garden" without cutting any flowers, touching the mole, or getting hit by

The Coolest Paperboy
Get "perfect" throws for all newspapers in "The Paperboy" mission.

Careful Fighter
Complete any car crusher mission without taking any damage.

Experienced Delivery Boy
Don't loose any boxes in the "A job of Little Importance" mission.

Careful Parking Boy
Complete the "Parking Valet" mission without damaging any cars.

Sweet Cleaner
Complete the "Cleaning the Circus" mission without making King Klong angry.

Skilled Driver
Complete the "King Klong" mission without damaging the pickup.

Fast Rock Gatherer
Pick up all the special rocks in the mission "Singing in the Rocks" before any go down the drain.

Too Good to Compete
Keep first place in any racing mission for more than 1 minute… and win!

Perfect Timing
Finish any of Chuck's missions on foot without failing any obstacle nor taking any damage from traps.

Silver

The Suburbs
Complete all the Suburbs missions.

Town
Complete all the Town missions.

Desert
Complete all the Desert missions.

Car Crusher
Complete level 10 in the tasks "Car Crusher", "Battle in the Stadium" and "Desert Battle".

The Fastest Driver
Complete level 10 in all race tasks.

Curious Boy
Enter every open house and building in the game.

Flying Car
Perform a jump of 150 ft or more.

Careful Driver
Drive a car for 3 minutes without collisions.

Billboard Breaker
Jump through all the billboards in the game.

Slippery
Escape 40 times from your enemies by hiding in the trash cans.

Gold

I've Got Antennas!
Complete all the game missions, including all tasks.

Car Collector
Unlock all vehicles (excluding vehicles unlocked at the police station).

Sticker Collector
Collect all the stickers that you'll earn in the tasks.

Comic Fan
Find all the comic frames scattered around Planet 51.

Platinum

Platinum Trophy
All trophies have been unlocked.

Source = http://www.ps3trophies.co.uk//showthread.php?t=39414