Trim green tops from beets. Set greens aside. Wash beets well. Cover with water in a large saucepan and bring to a boil over high. Reduce heat to medium. Gently boil, partially covered, until beets are fork-tender, 30 to 35 min. Drain and rinse under cold water until cool enough to handle. Peel beets. Slice each into 6 wedges.
Whisk oil with vinegar, dill and salt in a large bowl. Wash beet greens. Pat dry and coarsely chop. Combine with beet wedges and dressing and toss until coated. Serve with Succulent citrus fish.