Here is the full list of all 51 Teenage Mutant Ninja Turtles: Mutants in Manhattan trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Unlock all Trophies
Transport gold bars 30 times
Protect 30 ATM machines
Transport 30 bags of money
Transport 30 Krang Bombs to a portal
Use any character at least 50 times
Obtain all Collectibles
Transport 10 Chemical Weapons to a Portal
Eat 100 pizzas
Defeat 10 Stone Warriors with turrets in Wingnut's stage
Dismantle Charms 30 times
Disarm 30 time bombs
Protect 10 Pizza Trucks
Traverse a total of 150 miles
Obtain 50% of all Collectibles
Complete a stage without being spotted once (outside of Missions)
Upgrade 30 Charm Effects
Detonate 100 drum cans (including proximity mines)
Destroy a rampaging car with a drum can
Defeat 5 enemies with both Turbo Mode and Berserk activated
Defeat the 4 Krangdroids with your conventional weapons in Mega Krang's stage
Survive the elevator section at the TCRI building without taking any damage
Complete Easy or Normal mode
Have all Turtles turn into zombies simultaneously by touching contaminated water
Obtain 25% of all Collectibles
Have Mikey do his co-op move finishing pose during the snapshots when a boss is defeated
Use Turtle Switching to defeat 1 enemy with all 4 Turtles
Complete Hard mode
Find the secret room in the TCRI building
Destroy 30 cameras and laser devices
Experience all of the Krang UFOs' status effects
Climb to the highest point in Karai's stage and do a little dance
Defeat Rocksteady and Bebop by letting them get run over by a train
Complete a gold bar mission without the carrier being hit even once
Have everyone perform a Communication Action during the snapshots when a boss is defeated
Traverse a total of 32 miles
Eat a pizza during the snapshots when a boss is defeated
Destroy a helicopter
Defeat a Secret Boss
Enter the Pizza Room during the snapshots when a boss is defeated
Activate the ceiling switch during the battle with Slash
Collect 10,000 Training Points
Defeat 5 enemies at once by blowing up a Foot Soldier carrying a bomb bag
Use a Combo Attack to defeat 6 enemies at once
Play online at least once
Hang out outside of an enemy hideout for at least 10 seconds
Defeat 5 enemies with 1 drum can
Traverse 1 mile in the Residential Area without touching the ground
Equip at least one Emblem to your profile
Grind rails for 300 feet
Complete the Tutorial