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