Cut the pork into 4 pieces and place in a deep pot. Add the water to the pot, cover, and cook over medium-high heat until the meat is tender, about 45 minutes to 1 hour. Remove the pork from the pot and chop into bite-sized pieces.
Warm the flour or corn tortillas. Spread some of the beans on each tortilla and top with some of the pork. Squeeze a wedge of lime over each tortilla. Add the cilantro, onion, salsa, and avocado.