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