Here is the full list of all 15 Don't Sink achievements.
Capture an island!
Begin your journey!
Spend 25,000 gold!
Lost to the seas only you can find him. Rumor has it he is somewhere in the main menu!
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.
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"
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.