Successfully complete one of the following tasks to get a trophy:

Completionist (Platinum): Unlock all other trophies.
Just a Scratch (Bronze): Use pit lane to repair your vehicle 50 times.
Not On My Watch (Bronze): Wreck a car in pit lane before the repair.
The Hard Way (Bronze): Finish 5 races without using pit lane.
Just That Good (Bronze): Finish 3 races without wrecking or using pit lane.
I Meant To Do That (Bronze): Drive over 15 oil slicks.
Watch Your Step (Bronze): Bump another car into an oil slick.
Didn't See You There (Bronze): Bump another car into a hazard.
Turbo Speed! (Bronze): Complete 50 Slingshot boosts.
It Still Counts! (Bronze): Wreck your car across the finish line.
Winner! (Bronze): Place 1st on the Daytona Oval.
Show-off (Bronze): Perform a donut and go on to win the race.
2 Birds, 1 Stone (Bronze): Make 2 Rivals at the same time.
Showboater! (Bronze): Drift around 75 turns.
High Score (Bronze): Score higher than 175,000 in a single race.
Sun Was In My Eyes (Bronze): Wreck your car 15 times.
Look Mom! (Bronze): Drive over 35 ramp jumps.
Stuntman (Bronze): Perform 5 barrel rolls in mid-air.
Rocketman (Bronze): Slingshot into 25 ramp jumps.
Beat The Clock! (Bronze): Earn a trophy on any time trial track.
Stylin' (Bronze): Customize any car with an unlocked paint job
Eat My Dust (Bronze): Place 1st in any race against your friend.
Good Effort! (Bronze): Finish a quick race season in any place but 1st.
The Real Deal (Bronze): Place 1st in a quick race season.
Friendly Rivalry (Bronze): Wreck your friend making him/her a rival.
Tough Guy (Bronze): Make 75 rivals.
Well Played (Bronze): Score higher than your friend in a quick race season.
Revenge! (Bronze): Score a payback.
That'll Learn Ya! (Bronze): Score 10 paybacks.
Light Touch (Bronze): Score 125 slams.
Unnecessary Roughness (Bronze): Score 250 slams.
Beatdown! (Bronze): Make 3 rivals in a single race.
Thrashing! (Bronze): Make 5 rivals in a single race.
Scenic Route (Bronze): Drive over oil, dirt, sand, gravel, water, and grass.
Hot Shot (Bronze): Place 1st in any race.
Learning The Ropes (Bronze): Complete the Rookie tier in championship mode.
Showing Promise (Bronze): Complete the Professional tier in championship mode.
World Traveler (Bronze): Unlock all race tracks.
Drive By Healing (Bronze): Boost through pit lane restore.
Piece Of Cake (Bronze): Complete 10 challenges.
Over Achiever (Bronze): Complete 5 challenges in a single race.
Domination! (Silver): Score higher than 225,000 in a single race.
Time To Spare (Silver): Earn a gold trophy on any time trial track.
Gotta Have 'em All (Silver): Unlock all vehicle paint jobs.
Lightning Reflexes (Silver): Drive in boost mode for 12 seconds or more in a race.
So Close (Silver): Earn silver trophies on all time trial tracks.
That All You Got? (Gold): Complete the legend tier in championship mode.
In The Groove (Gold): Avoid walls and track barriers to score 2 perfect laps in one race.
Perfectionist (Gold): Earn gold trophies on all time trial tracks.