Drain beets; reserve 1 cup juice. In saucepan combine vinegar, sugar, salt, cloves, onion and juice. Bring to a boil, stirring occasionally. Add the beets; simmer uncovered for 10 minutes. Put the shelled eggs into a wide-mouth half-gallon jar. Pour in beets and liquid. Cool, cover and refrigerate for At Least 24 hours. Turn jar occasionally to mix ingredients so eggs pickle evenly.