Trim excess fat from the pork shoulder and cut into 2-inch chunks.
In a slow cooker, combine the pork, orange juice, lime juice, minced garlic, diced white onion, cumin, oregano, chili powder, sea salt, and black pepper.
Cover and cook on low for 7 to 8 hours or on high for 4 to 5 hours until the meat is tender enough to shred with a fork.
Remove the pork from the slow cooker and shred using two forks, discarding any large pieces of fat.
Heat a non-stick skillet over medium-high heat and add the shredded pork with a splash of the cooking liquid, searing for 3-5 minutes until the edges are golden and crispy.
Warm the corn tortillas in a dry pan or over an open flame until pliable.
Divide the crispy carnitas between the tortillas and top with chopped cilantro and thinly sliced radishes.