Here is the full list of all 41 Skylanders SuperChargers trophies - there are 31 bronze, 5 silver, 4 gold and 1 platinum.
Solve 15 Live Wire Lock puzzles
Reach Portal Master Rank 25
Collect 43 Skystones
Defeat The Darkness on any difficulty
Earn all Land vehicle stars
Have at least 5 active Legendary Treasures in the Academy at once
Collect 10 Legendary Treasures
Beat The Bandit Train on any difficulty
Beat Vault of the Ancients on any difficulty
Beat Ridepocalypse Demo Derby on any difficulty
Beat Monstrous Isles on any difficulty
Beat Cap'n Cluck's Chicken HQ on any difficulty
Beat Gadfly Glades on any difficulty
Beat The Spell Punk Library on any difficulty
Reach Portal Master Rank 10
Beat Battlebrawl Island on any difficulty
Beat Land of the Undead on any difficulty
Beat The Cloud Kingdom on any difficulty
Beat The Cloudbreather's Crag on any difficulty
Collect 4 vehicle Mods
Fully upgrade a vehicle
Complete a Race level
Come in 1st place in any Race level on any difficulty
Beat The Rift to Skylands on any difficulty
Equip 3 different Mods on one vehicle
Equip your first Mod
Honk your first vehicle horn
Enter a vehicle in Co-Op mode
Defeat an enemy while SuperCharged
Earn all other trophies
Complete Story Mode on Nightmare difficulty
Reach Portal Master Rank 40
Reach Portal Master Rank 55
Reach Portal Master Rank 70
Come in 1st place in any Race level on each difficulty
Win 15 Games of Skystones: Overdrive
Earn 6 gold Emblems
Achieve gold on 12 Emblems
Complete 10 quests given by Hugo
Complete 10 quests given by Tessa
Fully complete a Driver quest from Buzz