Place the water and turkey legs in an 8-quart pot over medium-high heat. Cover, bring to a boil, and allow to simmer for 10 minutes.
In the meantime, remove any large stems from the greens and wash them thoroughly; do so in a sink with at least 5 inches of water. Moving the leaves around in the water and allowing them to sit for a few minutes to allow the sand or dirt to fall to the bottom of the sink. Once clean, chop pieces in half. You should have 2 pounds of greens once they are stemmed. (Weigh the greens after stemming, but before washing.)
Once the turkey legs have simmered for 10 minutes, add the greens, salt and sugar, reduce the heat to low, cover, and allow to simmer gently for 45 minutes or until the greens are tender. Move the greens around every 10 to 15 minutes. Taste and season with additional salt, if desired. Serve immediately.