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.
Collect all Avengers characters in the game (Single Player)
Collect all traditionally evil mutants (Single Player)
Unlock Black Cat (Single Player)
Collect all Iron Man armors (Single Player)
Complete House Party Protocol
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
Defeat 100 enemies as the Thing
Complete Level 13 - Magnetic Personality
Complete Level 12 - Rapturous Rise
Complete Level 11 - Taking Liberties
Complete Level 10 - That Sinking Feeling
Complete Level 9 - Doctor in the House
Collect Howard the Duck (Single Player)
Complete Level 8 - Juggernauts and Crosses
Complete Level 7 - Bifrosty Reception
Complete Level 6 - Red Head Detention
Team up Captain America with Human Torch (Co-op)
Complete Level 5 - Rebooted, Resuited
Play as Agent Coulson
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
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 Doc Ock, Sandman, Mysterio, Kraven the Hunter, Electro and Vulture (Single Player)
Collect all traditionally heroic mutants (Single Player)
Turn into Stan Hulk
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)