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