LEGO Batman 3: Beyond Gotham has 71 trophies - 62 bronze, 4 silver, 4 gold and 1 platinum.The base game contains 41 trophies, and there are 6 DLC packs containing 30 trophies.
Complete Batman 75 level
Complete Batman 75 level with all Minikits unlocked
Complete Batman 75 level after achieving True Hero status
Set both Free Play characters as Batman (Sinestro Corps) and Vampire Batman
Complete Batman's special Anniversary Dance Puzzle as Batman (1966)
Complete Man of Steel level
Complete Man of Steel level with all Minikits unlocked
Complete Man of Steel level after achieving True Hero status
Set both Free Play characters as General Zod and Superman (Man of Steel)
Play as Krypto in the Man of Steel level
Complete the Dark Knight level
Complete the Dark Knight level with all Minikits unlocked
Complete the Dark Knight level after achieving True Hero status
Set both Free Play characters as Bane (Dark Knight Rises) and Scarecrow (Batman Begins)
Defeat Batman (Dark Knight Trilogy) as the Joker (Nurse) character
Complete Arrow level
Complete Arrow level with all Minikits unlocked
Complete Arrow level after achieving True Hero status
Set both Free Play characters as John Diggle and Felicity Smoak
Defeat 20 enemies on the Island by using a bow and arrow weapon
Complete Bizarro level
Complete Bizarro level with all Minikits unlocked
Complete Bizarro level after achieving True Hero status
Set both Free Play characters as Darkseid and Desaad
Play as Darkseid on the Moon
Complete The Squad level
Complete The Squad level with all Minikits unlocked
Complete The Squad level after achieving True Hero status
Set both Free Play characters as Amanda Waller and Harley Quinn (The Squad)
Complete any hub race using Harley Quinn's Motorcycle