Step #1 Place the peeled eggs & onion slices in a 1-quart glass jar.
Step #2 In a saucepan bring the beet juice or water, salt, vinegar, sugar & garlic cloves; bring to a boil stirring for a couple of mins until the sugar & salt is dissolved; remove this from heat & let cool (about 30 mins).
Step #3 Pour the vinegar mixture over the eggs & cover tightly.