Season the pork shoulder with sea salt, black pepper, cumin, oregano, and minced garlic, rubbing the spices into the meat thoroughly.
Place the seasoned pork in the slow cooker and pour the orange juice over it to provide moisture and natural acidity for tenderizing.
Cover and cook on low for 7 to 8 hours until the meat is tender enough to fall apart easily with a fork.
Remove the pork from the slow cooker, shred it using two forks, and discard any large pieces of rendered fat.
Heat a non-stick skillet over medium-high heat and sear the shredded pork for 3-5 minutes until the edges become golden and crispy.
Warm the corn tortillas in a dry pan or over an open flame for a few seconds on each side until pliable.
Assemble the tacos by dividing the crispy pork between the tortillas and topping with diced red onion, sliced radishes, and fresh cilantro.
Squeeze fresh lime juice over the tacos just before serving to brighten the savory flavors.