Drain juice from canned beets into a large container with a lid; stir in apple cider vinegar, sugar, and water until sugar has dissolved. Mix sliced beets, hard-cooked eggs, and sweet onion into the liquid; add more water so liquid covers eggs completely if needed. Cover container and refrigerate for 1 to 3 days, stirring the eggs and beets twice daily. The longer they soak, the deeper the eggs' color will be.