Here is the full list of all 51 Ace Combat: Assault Horizon trophies - there are 38 bronze, 10 silver, 2 gold and 1 platinum.
Rescued Major Illich from enemy captivity.
Successfully focused on 3 targets.
Obtained and destroyed 10 enemies in a helicopter.
Removed enemy presence from the oil field and the base.
Flew beneath a falling chimney.
Successfully pursued 3 enemies with counter maneuvers.
Took out a large number of hostiles as the door gunner.
Destroyed 5 hostile vehicles from the air as the door gunner.
Ejected from a damaged aircraft.
Destroyed an enemy aircraft using only the standard machine gun while piloting an aircraft.
Took down a hostile fighter with a charged homing missile.
Obtained all Trophies.
Protected your allies using the gunship, and led a successful attack on the base.
Attempted an emergency landing in a damaged aircraft.
Disintegrated enemy bombers in mid-air, keeping damage to the city to a minimum.
Eliminated enemy threat from the Suez Canal.
Prevented enemy from using Trinity to destroy Derbent.
Successfully took off to protect allies amid heavy hostile fire.
Sank the enemy fleet and saved the Russian Prime Minister.
Destroyed the ICBMs.
Destroyed the air defense system, opening the way for allied pilots.
Protected Moscow from destruction, freeing it from enemy control.
Alleviated the attack on Miami and helped Guts bail out.
Pursued the enemy and shot down Major Illich.
Protected Washington D.C. from the threat of Trinity, and returned alive.
Cleared all missions.
Took down 3 hostiles in a row with an assault chain.
Wiped out hostile ground forces with ASM.
Defeated hostiles with all 3 of the gunship's weapons.
Took down 5 hostiles with a direct shot.
Successfully switched from defense to offense 10 times with counter maneuvers.
Flew through the big hotel's gates.
Destroyed all radar missile defense systems in a short period of time.
Managed to get Sova 1 to land safely.
Defeated a large number of enemies while flying a bomber.
Took down 5 hostiles in a row with an assault chain.
Shot down a large number of hostile players in competitive online.
Used DFM support or ASM support to join a flight member.
Saved an ally being targeted by hostile players in DFM in competitive online.
Sortied for 50 hours in competitive online or mission co-op.
Cleared all levels in mission co-op.
Joined the same DFM with two others and shot down a hostile (mission co-op).
Piloted all aircraft in the game.
Cleared 1 level in mission co-op.
Used DFM to destroy 10 airborne enemies in competitive online.
Used ASM to destroy 30 ground enemies in competitive online.
Used an attack helicopter and destroyed 10 missiles or bombs in competitive online.
Played on all maps in competitive online.
Obtained an A rank for every mission (free mission).
Obtained all MVPs.
Used Trinity to wipe out the enemy (free mission).