Here is the full list of all 47 Danganronpa 2: Goodbye Despair trophies - there are 34 bronze, 9 silver, 3 gold and 1 platinum.
Cleared Island Mode once
Collected every possible present
Filled in every page of every character's Report Card
Filled in every page of Nekomaru's Report Card
Filled in every page of Kazuichi's Report Card
Filled in every page of Nagito's Report Card
Filled in every page of Fuyuhiko's Report Card
Filled in every page of Gundham's Report Card
Filled in every page of Teruteru's Report Card
Filled in every page of Hiyoko's Report Card
Filled in every page of Ibuki's Report Card
Filled in every page of Peko's Report Card
Filled in every page of Mahiru's Report Card
Filled in every page of Akane's Report Card
Filled in every page of Byakuya's Report Card
Cleared all stages of Magical Miracle Girl Monomi
Finished every chapter
Hajime Hinata breaks through level 99
Finished Chapter 5
Filled in every page of Sonia's Report Card
Finished Chapter 4
Collected 999 Monocoins
Finished Chapter 3
Found half of the Hidden Monokumas
Fully raised every type of pets
Filled in every page of Chiaki's Report Card
Filled in every page of Mikan's Report Card
Finished Chapter 2
Hajime Hinata breaks through level 50
Break through 10,000 total number of steps
Obtained all types of items in vending machine
Cleared a class trial without using your Concentration skill once
Cleared a class trial without taking any damage
Break through 5000 total number of steps
Challenged vending machine 100 times
Collected 50 unique presents
Finished Chapter 1
Cleared a class trial without having to retry once
Fully raised one type of pet
Finished the prologue
Earned every other trophy in the game
Found every Hidden Monokuma
Saw every possible Island Mode ending
Collected every possible item in Magical Miracle Girl Monomi
Unlocked all gallery items
Destroyed 100 white noise lines across all class trials
Destroyed 500 white noise lines across all class trials