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