Here is the full list of all 42 The Amazing Spider-Man trophies - there are 23 bronze, 16 silver, 2 gold and 1 platinum.
Unlock all Trophies
Collect all magazines
Collect all hidden Tech Pieces
Collect all Oscorp Manuals
Collect all audio evidence
Collect all 700 Spider-Man Comic Pages
Defeat 1000 enemies
Achieve a combo streak of 42
Immobilize 6 enemies simultaneously with web
Acquire all upgrades
Clear all car chases
Complete the game on super hero difficulty
Complete the game on human difficulty
Complete the game on hero difficulty
Defeat Lizard
Defeat Nattie
Rescue Alistaire Smythe
Defeat the S-03
Rescue all infected civilians
Resolve all police deadlocks
Complete all Oscorp Secret Research Labs
Clear the second fight against the Hunter robots
Return all escapees to the police
Defeat Felicia
Defeat Scorpion in the city
Perform a Web-Rush punch
Defeat 500 enemies
Defeat the S-02
Defeat Scorpion in quarantine
Defeat 100 enemies by performing Stealth Takedowns
Destroy a Seeker before it can call a Hunter
Clear the first fight against the Hunter robots
Defeat a Hunter without using your Web-Shooters
Defeat Vermin
Defeat 50 enemies by performing Stealth Takedowns
Defeat 100 enemies
Perform 25 Signature Moves
Save a hostage caught in a petty crime
Chain 10 Web-Rushes in the city
Defeat Rhino in the city
Defeat the S-01 without touching the ground
Defeat the S-01