Here is the full list of all 25 Zone of the Enders: The 2nd Runner HD Edition trophies - there are 3 bronze, 16 silver, 5 gold and 1 platinum.
Collect all trophies
Beat the game with a ranking of A
Unlock all the frames
Clear Zoradius
Find all 20 Ex-Missions
After the initial Vic Viper battle, defeat all of the Naritas in under 90 seconds
Beat the game with a ranking of S
Earn a Ranking of SS at Aumaan Crevasse
Defeat the 5 BAHRAM Battleships in less than 6 minutes
Reveal Ken's alternate outfit
Earn a Ranking of SS at Vascilia Battle
Defeat Aumaan Anubis
Defeat Anubis
Acquire Jehuty Ver. 2
Defeat Zakat
Defeat Inhert
Defeat an enemy by using the shafts at Fort City
Defeat the Viola AI for the final time
Defeat the train in less than 5 minutes
Defeat Vic Viper (Leo)
Find Taper in less than 4 guesses
Win your first encounter against the Viola AI
Complete all of the in-game tutorials
Defeat Ardjet
Acquire Jehuty