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