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