Place the pork shoulder, chopped white onion, minced garlic, orange juice, lime juice, cumin, oregano, sea salt, and black pepper into a slow cooker.
Cover and cook on low for 7-8 hours or on high for 4-5 hours until the pork is tender and easily pulls apart.
Remove the pork from the slow cooker and shred it thoroughly using two forks.
Heat the olive oil in a large cast-iron skillet over medium-high heat.
Add the shredded pork to the skillet in a single layer and sear for 3-5 minutes without stirring until the bottom is crispy and golden brown.
Warm the corn tortillas in a dry pan or over an open gas flame until pliable and slightly charred.
Thinly slice the radishes and roughly chop the fresh cilantro.
Assemble the tacos by dividing the crispy pork between the tortillas, then top each with a dollop of Greek yogurt, sliced radishes, and cilantro.