Here is the full list of all 51 The LEGO Movie 2 Videogame trophies - there are 37 bronze, 12 silver, 1 gold and 1 platinum.
Unlock Benny
Complete the Harmony City Level
Unlock MetalBeard
Collect 100 Items in the Game
Complete the Systarian Jungle Level
Defeat the Systarian Jungle Boss
Unlock Unikitty
Play as a Minidoll for the First Time
Complete the Old West
Shoot 50 Stickers with the Sticker Gun
Open 50 Relics
Collect 1,000,000 Studs
Complete the Asteroid Field Level
Collect 1000 Brick Pickups
Unlock Rex
Complete the Syspocalypstar Sandbox Tutorial
Open your first duplicate relic
Buy Something in a Shop
Open your First Relic
Complete the Apocalypseburg Level
Defeat the Apocalypseburg Boss
Do a build attack
Open a Discovery Chest
Unlock Lucy
Unlock all Trophies in The LEGO® Movie 2 - Videogame
Collect All Master Pieces on Apocalypseburg
Collect all Master Pieces in the Asteroid Field
Collect all Master Pieces in the Systarian Jungle
Collect all Master Pieces in Harmony City
Complete the Sorting Area Level
Defeat the Sorting Area Boss
Collect all Master Pieces in the Sorting Area
Complete The Ceremony Level
Collect all Master Pieces in The Ceremony
Complete Classic Bricksburg
Collect all Master Pieces in Classic Bricksburg
Collect all Master Pieces in the Old West
Complete Middle Zealand
Collect all Master Pieces in Middle Zealand
Complete Planet Unikitty
Collect all Master Pieces on Planet Unikitty
Complete the Planet Sparkles Level
Collect all Master Pieces on Planet Sparkles
Complete the Main Story
Unlock Batman
Unlock Sweet Mayhem
Unlock a Gold Character Variant
Build 20 Buildings in Syspocalypstar
Collect 100 Characters in the Game
Complete the Game to 100%
Try and place an object somewhere you can't, while on Syspocalypstar.