Here is the full list of all 51 Marvel's Avengers trophies - there are 41 bronze, 7 silver, 2 gold and 1 platinum.
Earn all Trophies
Fully upgrade any gear item
Complete 50 Hive missions
Complete HARM Challenges I to V
Purchase an item from two different faction vendors
Open 50 Cache strongboxes
Complete an Elite Heroic Hive
Reach Hero Level 50 and purchase all skills for any Hero
Rescue 100 AIM prisoners
Reach Power Level 150 with any Hero
Complete five Hive missions
Fully upgrade a major artifact
Complete the "Iconic Avengers" mission chain
Earn a total of 250 Hero Levels across the entire Hero Roster
Reach rank 25 in any faction
Equip all Legendary or better gear with any hero
Complete 15 Villain Sectors
Complete the "A Global Offensive" mission chain
Complete 100 assignments
Earn a 100% rating for any War Zone at Challenge IV rating
Complete 30 War Zones at Challenge III or higher rating
Break into 30 Depots
Defeat MODOK and the Kree
Reunite the Avengers
Collect 500 gear items
Collect 50 intelligence files
Reach Hero Level 5 with 5 different Heroes
Rescue Captain America
Reach the AIM space station
Stop the Helicarrier from crashing into New York City
Rescue Inhumans from the research facility
Recruit Black Widow
Open 100 strongboxes
Complete 10 assignments
Locate the Ant Hill
Destroy the AIM arc reactor
Complete any mission in under three minutes
Earn a 100% rating on a mission without any team member being downed
Defeat 50 enemies with Assault Heroic or Ultimate Heroic abilities
Defeat any 20 different enemy types
Recruit Tony Stark
Collect three Artifacts
Recover the SHIELD Protocols
Earn a five star rating on an objective without any team member taking damage
Reach a combo of 20 hits or higher
Recruit Bruce Banner
Discover the location of the Chimera
Escape the clutches of AIM in New Jersey
Defeat 10 or more enemies with a single Heroic ability activation
Reach the VIP balcony
Collect a full comic set