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