Here is the full list of all 31 Mercenaries Wings: The False Phoenix trophies - there are 17 bronze, 7 silver, 6 gold and 1 platinum.
Achieve all trophies
Finish chapter 1
Finish chapter 3
Finish chapter 7
Finish chapter 10 of the mercenary route
Finish chapter 12 of the mercenary route
Finish chapter 15 of the mercenary route
Finish chapter 17 of the mercenary route
Finish chapter 20 of the mercenary route
Finish the final chapter of the mercenary route
Finish chapter 10 of the Royal Army route
Finish chapter 12 of the Royal Army route
Finish chapter 15 of the Royal Army route
Finish chapter 17 of the Royal Army route
Finish chapter 20 of the Royal Army route
Finish the final chapter of the Royal Army route
Trade a puzzle piece for rare equipment
Synthesize a magic item
Synthesize a magic item that costs over 20000G
Clear EX stage 01
Clear EX stage 02
Clear EX stage 03
Clear EX stage 04
Clear the Dungeon of Trials
Deal over 999 damage to an enemy of LV40 and above in one blow
Have a party member reach LV99
Have a party member change to a intermediate class
Have a party member change to a advanced class
Have a party member change to a special class
Clear the game in HARD difficulty
Clear the game in MANIAC difficulty