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