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
Beat all the Staff Ghosts in Time Attack
Unlock every Character in the game
Get a Podium Finish in every Grand Prix tournament
Get a Podium Finish in every Grand Prix tournament on Expert difficulty
Finish 1st in every Grand Prix tournament on Expert difficulty
Visit every location in the game
Earn your Star License
Unlock Mirror Grand Prix mode
Complete an event with 4 local friends
Finish 1st in a Grand Prix tournament
Finish 1st in a Grand Prix tournament at Expert difficulty
Collect every Star in World Tour
Do 5 overtakes in a single Drift
Complete the Dream Valley Ring Race and pass every Ring as NiGHTS or Reala
Beat 01:11.16 in Time Attack as Vyse in Rogue's Landing
Beat your first Staff Ghost in Time Attack
Earn your S Class License
Roll Left, Roll Right, Backflip, Forward Flip and land as a car or boat
Do a Boost-Start in each vehicle mode
Hit 1st, 2nd and 3rd place with a Swarm attack
Complete a World Tour event on Expert difficulty
Unlock Superstar Showdown in World Tour
Earn your A Class License
Get a Perfect Drift score on a Drift Challenge event
Do a Level 3 Air-Drift
Evade or Block a homing-weapon 3 times in a Race
Finish a Battle Race without losing any lives
Get 10 hits by firing weapons backwards in a single event
Hit an opponent with a weapon while looking backwards
Hit 2 opponents with a single Hot Rod Blast
Earn your B Class License
Absorb a weapon with the Glove and fire it back at your attacker
Do 10 Stunt Combos in a single event
Get a total of 20 hits with weapons in a Race
Win an event with a Mod equipped
Collect 10 Stars in World Tour
Freeze an opponent with Ice from at least 100 meters away
Finish 1st, 2nd, 3rd and 4th with local friends in a 10 player Race
Do a Reckless Boost
Triple-Stunt while transforming into a car or boat
Detonate the Hot Rod at the very last second
Level-up a character
Score 90% accuracy with aimed weapons in an event
Go All-Star!
Win a Matchmaking game
Manually select a Random character for a Matchmaking game
Finish 0.5 seconds ahead of an opponent in a Race
Do a 10 second Drift as Sonic
Finish 1st in a Race without getting hit by weapons