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