Here is the full list of all 28 Nantucket achievements.
Kill an enemy just after he killed one of your man
Repel a pirate board
Take a cabin boy up to level 10
Complete 10 delivery quests
Hunt your first whale
Navigate 21.600 nautical miles
Level all the ship compartments up to their maximum
Complete all the side quests
Enter a city with 3 or more sick men in your crew
Hunt every type of sea creature
Hunt 100 whales
Kill a legendary creature
Discover all the whaling areas and routes
Track back 10 lost ships
Have at least 5 crew members with the "Sodomite" trait on your ship
Reach level 5
Reach level 10
Reach level 15
Reach level 20
Kill Moby Dick
Amass $10.000
Complete "Finding Rachel" quest
Complete "Blind secrets" quest
Visit all the cities
Create 5 safe docks