Season the pork shoulder thoroughly with chili powder, cumin, garlic powder, onion powder, sea salt, and black pepper.
Place the seasoned pork in a slow cooker or heavy pot and cook on low heat until the meat is tender and easily shredded with a fork.
Shred the cooked pork using two forks, removing and discarding any large pieces of excess fat.
Heat the avocado oil in a large cast-iron skillet over medium-high heat and add the shredded pork, pressing it down to create a crispy, golden-brown crust.
While the pork is crisping, whisk together the Greek yogurt and lime juice in a small bowl until the mixture is smooth and pourable.
Warm the corn tortillas in a dry pan or directly over a low gas flame until they are pliable and slightly charred on the edges.
Assemble the tacos by dividing the crispy pork between the tortillas, then topping with the lime crema, sliced radishes, and fresh cilantro.