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