Season the pork shoulder thoroughly with the sea salt, black pepper, ground cumin, and dried oregano.
Place the seasoned pork into a slow cooker and add the minced garlic, diced white onion, and orange juice.
Cover and cook on low for 7 to 8 hours until the meat is tender enough to be easily pulled apart.
Remove the pork from the slow cooker and shred it using two forks, discarding any excess fat.
Heat a large non-stick skillet over medium-high heat and sear the shredded pork for 3 to 5 minutes until the edges become golden and crispy.
Warm the corn tortillas in a dry pan or over an open flame until soft and slightly charred.
Divide the crispy carnitas among the tortillas and garnish with sliced radishes, fresh cilantro, and a squeeze of lime juice.