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