Activate the following cheats by entering the corresponding codes:

Bronze trophies
Open Mic Knight - Complete Gotham Theatre.
The Joke's on you! - Complete The Joker Getaway.
A-maze-ing Chase - Complete Arkham Estate.
Dishonourably Discharged! - Complete Arkham Asylum.
A Winning Formula - Complete ACE Chemicals.
Road to Ruin - Complete Juggernaut Chase.
Deconstructive Criticism - Complete The Batcave.
Flying Lessons - Complete Assault the VTOL.
Behind Enemy Lines - Complete Attack on LexCorp.
Frequent Flyer - Complete Robot Sky Battle.
Hero in Train-ing - Complete Gotham Metro.
Double-crossed! - Complete Brawl at City Hall.
Hostile Takeover - Complete Wayne Industries.
Justice League, Assemble! - Complete The Final Battle.
The Big Brick Theory - Create your first character in the Character Customiser.
Bane of my Life - Take down Batman with Bane. (Single Player Only)

Silver trophies
All Change! - Swap characters using Super Freeplay.
Sound Advice - Collect all the Sound Bite tokens.
Call Shotgun - Stun an enemy using Commissioner Gordon's trusty weapon and finish them. (Single Player Only)
Taking the Plunge - Help an enemy off a ledge in Wayne Industries.
Siamese Bat - As Catwoman, use the Stealth Takedown ability to attack Batman. (Single Player Only)
Batter Up! - Using the Batman glide ability, spend 5 seconds or more in the air.
True Hero - Achieve a True Hero stud total.
Starter Pack - Unlock all the Ability packs for the Character Customiser.
Brick by Brick - Collect all the Red Bricks.

Gold trophies
Super Friends - Collect all the Hero characters.
Bad Influence - Collect all the Villain characters.
Happy Daze - Stun 100 enemies.
Unbreakable - Finish a level without losing all your hearts.
MVP - Complete every arena in Justice League Mode.
Justice is Served - Win gold in every arena in Justice League Mode.

Platinum trophy
Complete Hero - Earn all Bronze, Silver, and Gold trophies.