Here is the full list of all 53 LEGO Marvel Super Heroes: Universe in Peril trophies - there are 42 bronze, 9 silver, 1 gold and 1 platinum.
Collect all trophies
100% the game
Complete all Challenges
Defeat Doctor Doom with every member of the Fantastic Four
Tag in the Punisher twice while playing as Spider-Man
Collect all characters
Unlock the Creator
Collect all Red Bricks
Team up Beast and Star-Lord
Tag in War Machine while playing as Iron Man
Unlock the Future Foundation characters
Defeat the Green Goblin as Gwen Stacy
Tag in Wolverine to finish the Abomination
Unlock all Wolverine variants
Unlock all Spider-Man suits
Beat the Green Goblin as Scarlet Spider (Classic)
Complete all challenges in 20 levels
Tag in Pepper Potts (Rescue) while playing as Tony Stark
Unlock all Iron Man suits
Beat a Raptor as Scarlet Spider (Classic)
Walk past Deadpool as Deadpool
Complete Stark Tower A, B and C with Hawkeye as a tag partner
Beat Doctor Octopus as Aunt May
Beat Loki as Agent Coulson in Asgard
Beat the 3 Loki holograms as Thor in Galactus B
Complete Heroes vs. Galactus C with the Silver Surfer
Complete Heroes vs. Galactus B with the Human Torch
Complete Heroes vs. Galactus A with the Thing
Finish Heroes vs. Galactus
Finish all levels
Finish Asteroid M: Showdown
Beat Abomination as Red Hulk
Finish Asteroid M: Space
Finish Island M
Finish New York Power Station
Finish Doctor Doom’s Tanker
Call in Daredevil with only one heart remaining
Beat Doctor Octopus with Human Torch in your team
Beat the Red Skull as Captain America and Captain America (WW2)
Finish Castle Doom
Finish X-Mansion
Finish Asgard
Tag in Thor to battle Loki
Finish Hydra Base
Have Captain America and Human Torch on the same screen
Beat Iron Man (Hulkbuster) with the Hulk
Finish Stark Tower
Complete all challenges in one level
Finish The Raft
Finish Oscorp
Finish Baxter Building
Finish Sand Central Station
Finish a level as Banner