Here is the full list of all 31 Mercenaries Wings: The False Phoenix achievements.
Unlock all Achievements
Clear Chapter 1
Clear Chapter 3
Clear Chapter 7
Clear Breakaway Route Chapter 10
Clear Breakaway Route Chapter 12
Clear Breakaway Route Chapter 15
Clear Breakaway Route Chapter 17
Clear Breakaway Route Chapter 20
Clear Breakaway Route Final Chapter
Clear Military Route Chapter 10
Clear Military Route Chapter 12
Clear Military Route Chapter 15
Clear Military Route Chapter 17
Clear Military Route Chapter 20
Clear Military Route Final Chapter
Trade a puzzle piece for rare equipment
Create a magic item through synthesis
Synthesize 20000G worth of magic items
Clear stage EX01
Clear stage EX02
Clear stage EX03
Clear stage EX04
Clear stage EX05
Exceed 999 damage to an enemy over Lv.40
Level up a character to Lv.99
Class change a character to an Intermediate class
Class change a character to an Advanced class
Class change a character to a Special class
Clear the game in HARD difficulty
Clear the game in MANIAC difficulty