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