Here is the full list of all 44 Pirates of Black Cove achievements.
Killed 20 melee soldiers using ranged units
Bought first special weapon
Complete all Pirate Story missions
Overdrank grog 5 times
Managed to reach Sirens
Killed 20 ranged soldiers using melee units
Picked up a total of 50 ingredients for the Mad Alchemist
Bought the first visual upgrade for ship
Complete the first pirate faction mission.
Found first joke
Visited a colony
Complete the first storyline mission
Sunk 100 ships with mortar
Used 99 bottles of grog
United all the factions
Finished the game
Stunned 10 enemy soldiers simultaneously with stink bomber
Found all jokes in the game
Complete all Buccaneer Story missions
Complete all Corsair Story missions
Destroy 20 banks
Spent 30 minutes on the world level without participating in any mission
Constructed all buildings in all strongholds
Used the human catapult
Successfully captured a ship
Sink 5 Black Cove ships!
Sunk 100 ships with basic cannons
Player ship destroyed (from max hp) by one broadside from a Black Cove ship
Sailed at the seas while under 20% of ships hitpoints for 5 minutes
All different unit types under control at the same time
Unlocked all special weapons
Found 50 Eyepatches of the Beholder
Met the ghosts
Found all blueprints
Created a total of 10 potions with the Mad Alchemist
Owned 20 ships at the same time
Hired a total of 50 units
All available unit spots filled, including heroes
Unlocked all ship upgrades.
Captured a ship without losing any ship health
Completed chapter 1
Completed chapter 2
Completed chapter 3
Completed chapter 4