Here is the full list of all 50 Marvel's Spider-Man: Miles Morales trophies - there are 37 bronze, 10 silver, 2 gold and 1 platinum.
Scroll through the entire Social Feed at the end of the story
100% complete all districts
Collect all Postcards
Save Harlem
Walk through Miles and Phin's past
Beat Phin at the rocket launch mini-game
Defeat 50 enemies while Camouflaged
Defeat Prowler
Pay respects at Jefferson Davis' grave in Harlem
Defeat Roxxon Rhino
Perform 25 Wall Takedowns
Collect all Sound Samples and recreate the Davis Brothers Mix
Complete all FNSM app requests
Pay your respects to a legend in the Upper West Side
Craft 10 Upgrades
Shut down all Underground Hideouts
Open all Underground Caches
Shut down all Roxxon Labs
Collect all Time Capsules
Unravel a criminal conspiracy in Harlem
Chase Tinkerer through the city
Defeat 50 enemies with Remote Mine gadget
Perform a Venom Jump, then a Venom Dash on a single enemy
Use Venom Dash to throw an enemy into a group of three or more
Ride the derelict boat in southern Chinatown
Complete an Enemy Base without being detected
Complete the vault sequence in Underground Undercover
Complete the Final Test
Complete every Spider-Training Challenge once
Craft a Visor Mod
Investigate Roxxon's underground lab
Perform 100 Stealth Takedowns
Get Spectacular or better in a Spider-Training Stealth Challenge
Keep the bridge together
Get the trains running again
Perform a 100x Combo
Get Spectacular or better in a Spider-Training Traversal Challenge
Craft a Suit Mod
Get Spectacular or better in a Spider-Training Combat Challenge
Receive the Gift Suit
Ride Rhino through the mall
Collect all Trophies
Unlock all Skills
Purchase all suits
Perform 25 Ceiling Takedowns
Defeat 100 enemies with Venom attacks
Smash into 15 breakable objects while steering Rhino through the shopping mall
Apply a sticker and customize lighting while in Photo Mode
Complete all Bonus Objectives for every crime type
Complete the game on New Game+