Here is the full list of all 29 The Falconeer achievements.
Filled all mutagen slots for your Falcon
Found both biochemists and the weapons trader
Clocked fastest time on a racecourse
Completed the Prologue
Discovered a shrine or a temple
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
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 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 all 3 seachantresses
Bought a new type of weapon
Found all the fortified locations
Found all Imperial locations
Found all Civilian Free House locations
Found all Mancer locations
Took down 5 air targets in one mission
Took down 10 air targets in one mission
Destroyed 15 turrets in one mission
Sunk 3 ships in one mission