Trim any excess thick fat from the pork shoulder and rub the meat evenly with sea salt, black pepper, ground cumin, and dried oregano.
Place the seasoned pork into a slow cooker along with the minced garlic clove and the orange juice.
Cover and cook on low for 8 hours, or until the pork is tender enough to be easily pulled apart with a fork.
Remove the pork from the slow cooker and shred it into bite-sized pieces using two forks, discarding any remaining large pieces of fat.
Heat the olive oil in a large non-stick skillet over medium-high heat. Add the shredded pork in a single layer and press down with a spatula.
Sear the pork for 3-4 minutes without stirring until the bottom is deeply browned and crispy, then flip and sear for another 2 minutes.
While the pork crisps, warm the corn tortillas in a separate dry pan over medium heat for 30 seconds per side until pliable.
Divide the crispy carnitas between the two tortillas.
Top each taco with thinly sliced radishes, finely diced red onion, and fresh cilantro leaves.
Serve immediately with a squeeze of fresh lime juice over the top for brightness.