Place the beets into a saucepan with enough water to cover by 1 inch; bring to a boil. Reduce heat to medium-low, cover, and simmer until the beets are easily pierced with a fork, about 30 minutes.

Meanwhile, cook the bacon in a large, deep skillet over medium-high heat until evenly browned, about 10 minutes; transfer the bacon to a paper towel-lined plate to drain, reserving the bacon drippings in the skillet. Roughly chop the bacon and set aside.

Add the drained beets and red Swiss chard to the reserved bacon drippings; cover the skillet, place over medium heat, and cook until the chard is tender, 3 to 5 minutes. Stir the chopped bacon and frozen peas into the beet mixture; continue cooking until the peas are cooked through, about 5 minutes. Sprinkle the feta cheese over the mixture; stir. Serve hot.