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