Here is the full list of all 29 The Falconeer achievements.
Completed the Epilogue
Completed the Dunkle chapter
Converted a fortified position for the Mancer Order
Bought a new type of weapon
Unlocked all permits in every campaign
Took down 5 air targets in one mission
Converted a fortified position for the Imperium
Filled all mutagen slots for your Falcon
Discovered a shrine or a temple
Found all 3 seachantresses
Purchased all 5 falcon types from races
Completed the Prologue
Found all Mancer locations
Found all Civilian Free House locations
Completed the Cleftspire chapter
Completed the Shard chapter
Completed the Oberon's Reach chapter
Retured to the scene of the Nodbomb blast
Converted a fortified position for the Pirates
Bought all chants from the seachantresses
Clocked fastest time on a racecourse
Clocked the fastest time on all 5 racecourses
Discovered all the shrines and temples
Found both biochemists and the weapons trader
Found all the fortified locations
Found all Imperial locations
Took down 10 air targets in one mission
Destroyed 15 turrets in one mission
Sunk 3 ships in one mission