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