Here is the full list of all 28 Nantucket achievements.
Complete "Finding Rachel" quest
Kill an enemy just after he killed one of your man
Reach level 5
Navigate 21.600 nautical miles
Hunt your first whale
Repel a pirate board
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
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 10
Reach level 15
Reach level 20
Kill Moby Dick
Amass $10.000
Complete "Blind secrets" quest
Visit all the cities
Create 5 safe docks