Here is the full list of all 15 Don't Sink achievements.
Purchase the Man of War.
Capture and own 6 islands at the same time.
Complete at least 50% of all available quests.
Defeat 25 pirates at sea!
Spend 25,000 gold!
Purchase a better ship.
Build Cramton to completion starting from nothing.
Travel a total of 20,000 miles by sea.
Complete a sea voyage that is at least 2,000 miles in distance.
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 the side quest, "Tough Decisions"
Complete a sea voyage that is at least 1,000 miles in distance.
Capture an island!
Begin your journey!