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