Here is the full list of all 15 Don't Sink achievements.
Defeat 25 pirates at sea!
Capture and own 6 islands at the same time.
Lost to the seas only you can find him. Rumor has it he is somewhere in the main menu!
Capture an island!
Complete at least 50% of all available quests.
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.
Try to capture the ferret captain!
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!
Purchase the Man of War.