Here is the full list of all 52 Team Sonic Racing trophies - there are 40 bronze, 9 silver, 2 gold and 1 platinum.
Use the White Boost to destroy a projectile.
Complete Chapter 7 of Team Adventure Mode.
Complete Chapter 6 of Team Adventure Mode.
Gain 6 positions by using a single Yellow Drill.
Complete Chapter 5 of Team Adventure Mode.
Complete Chapter 4 of Team Adventure Mode.
Cause 3 opponents to spin-out by shunting them with a Pink Spikes active.
Block an incoming projectile with a Blue Cube.
Avoid every hazard created by a Gray Quake.
Use the White Boost to avoid being slowed down by terrain.
Modify a vehicle in the Garage.
Land a hit on enemy racers with each use of a x3 Orange Rocket.
Complete Chapter 3 of Team Adventure Mode.
Finish Frozen Junkyard without hitting any hazards or respawning.
Complete Chapter 2 of Team Adventure Mode.
Perform 100 Team Slingshots. (Across all Game Modes).
Perform a triple Stunt.
Complete Chapter 1 of Team Adventure Mode.
Perform a Team Ultimate 3 times in a single Race.
Perform 10 Team Slingshots in a single Race.
Cause an opponent to spin-out using a Red Burst.
Perform Team Item Transfer, Skimboost, Team Slingshot and Team Ultimate in a single Race.
Perform a Skimboost on a slow-moving Teammate.
Send an Item Box to a Teammate 5 times during a Race.
Collect all Trophies.
Perform a maximum Start Line Boost.
Finish an online race.
Earn every star in Team Adventure Mode Chapter 1.
Earn every star in Team Adventure Mode Chapter 2.
Earn every star in Team Adventure Mode Chapter 3.
Earn every star in Team Adventure Mode Chapter 4.
Earn every star in Team Adventure Mode Chapter 5.
Earn every star in Team Adventure Mode Chapter 6.
Earn every star in Team Adventure Mode Chapter 7.
Earn every star in Team Adventure Mode.
Collect all of the Team Adventure Mode Keys.
Complete all possible events on hard in any Team Adventure Mode chapter.
Complete all Team Adventure chapters on Hard difficulty.
Beat a friend's leaderboard time in Time Trial mode on any track.
Stay in a single Drift for over a minute.
Collect 20,000 Rings.
Travel 200 meters over slow-down surfaces with a single use of a Jade Ghost.
Spend 5,000 Credits.
Spin out 2 racers with Cyan Laser.
Unlock all of the Performance Mods (Except Legendary Mods).
Unlock all of the Vehicle Paint Kits.
Use the Violet Void to absorb a projectile and hit the racer who fired it.
Complete a Team Race with 2 additional local players on your Team.
While playing as Eggman, spin out Sonic 3 times in the same Race.
Achieve 1st place in a race with a fully customized Vehicle.
Avoid the effect of being hit by an Ivory Lightning.
Come first in an online race.