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