Cut off the stems, and peel the beets. Chop them in long pieces, small enough to fit through the grating tube on your food processor. Grate the beets with the food processor or box grater, until finely shredded.
Add the apple cider vinegar, water, rice vinegar, sugar, salt, and pickling seasoning to a medium pot, and bring to a boil. Then, lower the heat, and simmer for 10 minutes. Remove from the heat, and let cool.
Add the grated beets to 2 32-ounce, wide-mouth jars or a glass containers with a lid.
Pour the vinegar mixture over the shredded beets, making sure there is liquid covering the tops of the beets. You can add more water if necessary.
Let the pickled beets cool, then place the jars in the fridge for at least 24 hours before serving.