Here is the full list of all 45 LEGO Marvel Super Heroes achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Play as Agent Coulson
Unlock Black Cat (Single Player)
Destroy 100 vehicles in the Manhattan hub
Create a custom character
Complete Level 15 - The Good, the Bad and the Hungry
Complete Level 14 - A Doom with a View
Complete Level 13 - Magnetic Personality
Complete Level 12 - Rapturous Rise
Defeat 100 enemies as the Thing
Complete Level 11 - Taking Liberties
Complete Level 10 - That Sinking Feeling
Complete Level 9 - Doctor in the House
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
First time turning Mister Fantastic into a teapot
Complete first Helicarrier skydive
Complete Level 1 - Sand Central Station
Team up Captain America with Human Torch (Co-op)
Rescue Stan Lee from every peril (Single Player)
Transform into the Hulk 50 times
Collect 1,000,000,000 studs (Single Player)
Complete game 100% (Single Player)
Collect all Avengers characters in the game (Single Player)
Collect Doc Ock, Sandman, Mysterio, Kraven the Hunter, Electro and Vulture (Single Player)
Collect all traditionally heroic mutants (Single Player)
Collect all traditionally evil mutants (Single Player)
Collect all Iron Man armors (Single Player)
Turn into Stan Hulk
Complete House Party Protocol
Create a character called “Trevor” in the character customizer
Perform Hulk's special move on Loki
Read a comic in Deadpool's room on the Helicarrier
Unlock all animal-themed characters (Single Player)
Unlock all the Guardians of the Galaxy (Single Player)
Perform a special throwing move as Colossus on Wolverine
Drive to the Baxter Building as Magneto in the Magneto Mobile
Perform all big LEGO figure transformations
Unlock all True Believers (Single Player)
Collect Howard the Duck (Single Player)