Here is the full list of all 46 LEGO Marvel Super Heroes trophies - there are 38 bronze, 4 silver, 3 gold and 1 platinum.
Collect every trophy
Team up Captain America with Human Torch (Co-op)
Perform all big LEGO figure transformations
Drive to the Baxter Building as Magneto in the Magneto Mobile
Transform into the Hulk 50 times
Turn into Stan Hulk
Complete game 100% (Single Player)
Rescue Stan Lee from every peril (Single Player)
Collect all traditionally heroic mutants (Single Player)
Unlock all animal-themed characters (Single Player)
Collect all traditionally evil mutants (Single Player)
Unlock all the Guardians of the Galaxy (Single Player)
Unlock all True Believers (Single Player)
Create a character called “Trevor” in the character customizer
Create a custom character
Collect Doc Ock, Sandman, Mysterio, Kraven the Hunter, Electro and Vulture (Single Player)
Read a comic in Deadpool's room on the Helicarrier
Perform Hulk's special move on Loki
Collect 1,000,000,000 studs (Single Player)
Perform a special throwing move as Colossus on Wolverine
Collect all Iron Man armors (Single Player)
Collect all Avengers characters in the game (Single Player)
Complete House Party Protocol
Complete Level 15 - The Good, the Bad and the Hungry
Complete Level 14 - A Doom with a View
Complete Level 13 - Magnetic Personality
Collect Howard the Duck (Single Player)
Unlock Black Cat (Single Player)
Complete Level 12 - Rapturous Rise
Destroy 100 vehicles in the Manhattan hub
Complete Level 11 - Taking Liberties
Complete Level 10 - That Sinking Feeling
Complete Level 9 - Doctor in the House
Defeat 100 enemies as the Thing
Play as Agent Coulson
Complete Level 8 - Juggernauts and Crosses
Complete Level 7 - Bifrosty Reception
Complete Level 6 - Red Head Detention
Complete Level 5 - Rebooted, Resuited
Complete Level 4 - Rock up at the Lock up
Regenerate as Wolverine
Complete Level 3 - Exploratory Laboratory
Complete Level 2 - Times Square Off
Complete first Helicarrier skydive
First time turning Mister Fantastic into a teapot
Complete Level 1 - Sand Central Station