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