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