Mix water, vinegar, and sugar together in a bowl; add onion and cucumber. Set aside to marinate, at least 20 minutes.
Combine 2 hard-boiled eggs cut into bite-size pieces and beets together in a bowl.
Drain liquid from onion and cucumbers. Toss onion and cucumbers with beet mixture. Stir mayonnaise into beet mixture. Arrange sliced hard-boiled egg atop salad; sprinkle with dill, salt, and pepper.
