Here is the full list of all 15 Don't Sink achievements.
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.
Begin your journey!
Lost to the seas only you can find him. Rumor has it he is somewhere in the main menu!
Spend 25,000 gold!
Travel a total of 20,000 miles by sea.
Build Cramton to completion starting from nothing.
Complete the side quest, "Tough Decisions"
Capture an island!
Try to capture the ferret captain!
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.