Here is the full list of all 50 Final Fantasy Type-0 HD trophies - there are 38 bronze, 9 silver, 2 gold and 1 platinum.
Defeated a total of 20 enemies in combat simulation sessions.
Completed a secret training session.
Completed Chapter 2 "Raise the Vermilion Banner."
Forged a covenant with an Eidolon.
Collected 5 Knowing Tags.
Captured a chocobo.
Hatched 5 chocobos at the chocobo ranch.
Dodged 500 enemy attacks.
Landed Killsight strikes on 100 enemies.
Defeated 300 enemies.
Won a 5-battle chain encounter in the overworld.
Searched 3 surrendered imperial soldiers.
Took down 100 imperial soldiers.
Harvested 100 phantoma.
Completed a mission without allowing any casualties.
Cleared 3 missions.
Earned an S-Rank on a mission.
Defeated 100 enemies.
Sat in on one of Moglin's lectures.
Defeated an enemy with the explosion from a fuel tank.
Completed an SO.
Won an encounter in the overworld.
Talked with the moogles from all thirteen classes.
Completed Chapter 1 "War - Three Hours That Changed the World."
Landed Killsight strikes on 20 enemies.
Took down 20 imperial soldiers.
Obtained all trophies.
Completed Chapter 3 "Weapons of Mass Destruction."
Completed Chapter 4 "The Last Queen's Return to Oblivion."
Completed Chapter 5 "The First Battle of Judecca."
Completed Chapter 6 "Terra Mortis - Khalia's Decision."
Completed Chapter 7 "Fate of the Crystal - The Endless Battle."
Completed Chapter 8 "Verdict: Finis."
Earned the "An Army of One" bonus.
Earned the "A Lonely Battle" bonus.
Earned the "A Select Few" bonus.
Harvested 500 phantoma.
Forged covenants with 6 Eidolons.
Won 50 encounters in the overworld.
Cleared 15 missions.
Avoided the penalty for failing an SO.
Collected 25 Knowing Tags.
Acquired the airship "Setzer."
Shot down 50 enemies with the Setzer.
Captured 30 chocobos.
Hatched 100 chocobos at the chocobo ranch.
Defeated a total of 100 enemies in combat simulation sessions.
Liberated and visited all cities in the Dominion of Rubrum.
Completed a mission using only Primed cadets.
Searched 15 surrendered imperial soldiers.