I find beetroot is sweet enough, so I just use neat white vinegar. Cook beetroots, skins and tops will slide off, bring vinegar to boil but keep windows open or you'll get gassed lol
Take off heat as soon as it reaches the boil, pour into jars over tiny beets or sliced bigger ones, use a fork in the jar to prevent breaking.
Try to leave as long as you can as they are delish!