Here is the full list of all 39 Blackwake achievements.
200 headshots
Get 150 Cutlass kills
Get 150 Nock Gun kills
Get 150 Duckfoot kills
Get 150 Blunderbuss kills
Kill 100 enemy captains
Get 400 cannonball kills
Get 150 Musket kills
100 nose repairs
100 sails repaired
Repair 500 holes
Resupply 100 ammo crates
Kill 100 enemies with fires you started
Get 150 kills with a broken rum bottle
200 wins as captain of your crew
Get 150 Dagger kills
100 wins as captain of a galleon
200 kills with grapeshot
100 wins as captain of a hoy
100 wins as captain of a junk ship
As captain, help your crew land 5000 cannon hits
Get 150 Pistol kills
100 minutes spent pumping water
As captain, kill 1000 enemies by ship collision
Get 150 Rapier kills
100 wins as captain of a schooner
Get 150 Short Pistol kills
Get 50 mounted swivel gun kills
Get 150 Tomahawk kills
Get 150 Annley Revolver kills
Get 150 Grenade kills
100 wins as captain of a brig
100 wins as captain of a xebec
100 wins as captain of a cruiser
100 wins as captain of a bombvessel
100 wins as captain of a cutter
100 wins as captain of a bombketch
100 wins as captain of a carrack
100 wins as captain of a gunboat