Here is the full list of all 32 LEGO Batman 2: DC Super Heroes trophies - there are 16 bronze, 9 silver, 6 gold and 1 platinum.
Collect all trophies.
Win gold in every arena in Justice League Mode.
Collect all the Villain characters.
Complete every arena in Justice League Mode.
Unlock all the Ability packs for the Character Customiser.
Collect all the Red Bricks.
Collect all the Hero characters.
Collect all the Sound Bite tokens.
Take down Batman with Bane. (Single Player Only)
Stun an enemy using Commissioner Gordon's trusty weapon and finish them. (Single Player Only)
Swap characters using Super Freeplay.
As Catwoman, use the Stealth Takedown ability to attack Batman. (Single Player Only)
Complete The Final Battle.
Complete Wayne Industries.
Help an enemy off a ledge in Wayne Industries.
Complete Brawl at City Hall.
Finish a level without losing all your hearts.
Complete Gotham Metro.
Complete Robot Sky Battle.
Complete Attack on LexCorp.
Stun 100 enemies.
Create your first character in the Character Customiser.
Complete Assault the VTOL.
Complete The Batcave.
Complete Juggernaut Chase.
Complete ACE Chemicals.
Complete Arkham Asylum.
Complete Arkham Estate.
Using the Batman glide ability, spend 5 seconds or more in the air.
Complete The Joker Getaway.
Complete Gotham Theatre.
Achieve a True Hero stud total.