There are 21 secret trophies:
Under Their Noses (Silver): Shut down all Roxxon Labs.
Underground Undone (Silver): Shut down all Underground Hideouts.
Come at the King (Silver): Unravel a criminal conspiracy in Harlem.
Launch, Swing and Dive (Bronze): Get Spectacular or better in a Spider-Training Traversal Challenge.
Punching Pixels (Bronze): Get Spectacular or better in a Spider-Training Combat Challenge.
Dodging Light (Bronze): Get Spectacular or better in a Spider-Training Stealth Challenge.
Spider-Training: Complete (Bronze): Complete every Spider-Training Challenge once.
Pete’s First Villain (Bronze): Complete the Final Test.
Rhino Rodeo (Bronze): Ride Rhino through the mall.
Deep Cuts (Silver): Collect all Sound Samples and recreate the Davis Brothers Mix.
Hanging By A Thread (Bronze): Keep the bridge together.
The Core of the Problem (Bronze): Investigate Roxxon’s underground lab.
True Deception (Bronze): Complete the vault sequence in Underground Undercover.
The Harlem Express (Bronze): Get the trains running again.
Veloci-Skates (Bronze): Chase Tinkerer through the city.
Shared History (Bronze): Walk through Miles and Phin’s past.
Exploding Bulldozer (Bronze): Defeat Roxxon Rhino.
Family Drama (Bronze): Defeat Prowler.
Ultimate Sacrifice (Bronze): Save Harlem.
Competitive Spirit (Bronze): Beat Phin at the rocket launch mini-game.
A Gift From Pete (Bronze): Receive the Gift Suit.