Here is the full list of all 15 Don't Sink achievements.
Travel a total of 20,000 miles by sea.
Complete at least 50% of all available quests.
Defeat 25 pirates at sea!
Spend 25,000 gold!
Complete the side quest, "Tough Decisions"
Capture and own 6 islands at the same time.
Try to capture the ferret captain!
Lost to the seas only you can find him. Rumor has it he is somewhere in the main menu!
Capture an island!
Build Cramton to completion starting from nothing.
Purchase a better ship.
Complete a sea voyage that is at least 2,000 miles in distance.
Complete a sea voyage that is at least 1,000 miles in distance.
Begin your journey!
Purchase the Man of War.