Here is the full list of all 45 LEGO Batman 3: Beyond Gotham trophies - there are 30 bronze, 11 silver, 3 gold and 1 platinum.
Collect 100,000,000 studs
Unlock and purchase all hints
Perform 30 ground finishers
Complete all Free Play in the Watchtower
Complete chapter 15
Get maximum studs on all the Techno Access puzzles in all the levels
Complete chapter 14
Complete chapter 11
Complete chapter 13
Perform 20 counter attacks
Complete The Breach of Okaara in 3 loops or less
Complete chapter 10
Complete 100 Gold Brick challenges
Complete chapter 12
Complete chapter 9
Collect all the microchips
Complete all the Gold Brick Builds in the game
Complete chapter 8
Complete chapter 7
Complete chapter 6
Complete chapter 5
Complete chapter 4
Complete chapter 3
Complete chapter 2
Complete chapter 1
Discover the Killer Croc goon's prank
Complete all other trophies
Unlock all the suits in the game
Find all the Joker cards
Achieve 100% completion
Destroy all Joker LEGO objects
Destroy all Luthor LEGO objects
Destroy all Batman LEGO objects
Complete all Lantern Constructs
Complete all Free Play in the Batcave
View the credits without skipping them
Complete all Gold Brick challenges
Unlock and purchase all red bricks
Unlock and purchase all characters
Complete all the Gold Brick Combat challenges
Defeat 10 enemies with Superman's heat vision while flying
Complete The Containment Facility with the Batman 1966 Mode Red Brick active
Complete all the Gold Brick Space Combat Challenges in the game
Use the arcade machine
Discover Aquaman's tea party