In a medium saucepan, combine beet juice, vinegar, water, sugar, pickling spice, salt and onion. Bring to a boil over medium heat, stirring constantly just until the sugar dissolves. Reduce heat and simmer 10 minutes. Strain and cool at room temperature. In a large glass jar or container, pour beet juice mixture over whole hard-cooked eggs. Cover and marinate 2 to 3 days in the refrigerator before serving.