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