Here is the full list of all 51 Sonic & All-Stars Racing Transformed trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Earn every Trophy in the game
Earn your Triple-Star License
Finish 1st in every Grand Prix tournament on Expert difficulty
Get a Podium Finish in every Grand Prix tournament
Get a Podium Finish in every Grand Prix tournament on Expert difficulty
Unlock every Character in the game
Visit every location in the game
Beat all the Staff Ghosts in Time Attack
Earn your Star License
Collect every Star in World Tour
Unlock Mirror Grand Prix mode
Complete the Dream Valley Ring Race and pass every Ring as NiGHTS or Reala
Win a Matchmaking game
Survive a Twister attack without crashing or being hit
Get 10 hits by firing weapons backwards in a single event
Do 10 Stunt Combos in a single event
Get a Perfect Drift score on a Drift Challenge event
Finish a Battle Race without losing any lives
Do a Boost-Start in each vehicle mode
Earn your S Class License
Score 90% accuracy with aimed weapons in an event
Finish 1st in a Grand Prix tournament
Finish 1st in a Grand Prix tournament at Expert difficulty
Do 5 overtakes in a single Drift
Beat 01:11.16 in Time Attack as Vyse in Rogue's Landing
Beat your first Staff Ghost in Time Attack
Get a total of 20 hits with weapons in a Race
Freeze an opponent with Ice from at least 100 meters away
Complete a World Tour event on Expert difficulty
Hit 1st, 2nd and 3rd place with a Swarm attack
Finish 1st in a Race without getting hit by weapons
Unlock Superstar Showdown in World Tour
Earn your A Class License
Absorb a weapon with the Glove and fire it back at your attacker
Triple-Stunt while transforming into a car or boat
Roll Left, Roll Right, Backflip, Forward Flip and land as a car or boat
Raced in an ad hoc or Online game with Sonic, Tails, Amy, Shadow and Knuckles in the same race.
Manually select a Random character for a Matchmaking game
Evade or Block a homing-weapon 3 times in a Race
Earn your B Class License
Level-up a character
Do a Level 3 Air-Drift
Hit 2 opponents with a single Hot Rod Blast
Do a 10 second Drift as Sonic
Hit an opponent with a weapon while looking backwards
Do a Reckless Boost
Collect 10 Stars in World Tour
Win an event with a Mod equipped
Detonate the Hot Rod at the very last second
Finish 0.5 seconds ahead of an opponent in a Race
Go All-Star!