Season the pork shoulder evenly with sea salt, black pepper, chili powder, cumin, and garlic powder.
Place the seasoned pork in a slow cooker or pressure cooker and cook until the meat is tender and shreds easily.
Shred the cooked pork using two forks, discarding any large pieces of excess fat.
Heat avocado oil in a large cast-iron skillet over medium-high heat until shimmering.
Add the shredded pork to the skillet in a single layer and press down firmly to develop a deep, caramelized crust.
Squeeze fresh lime juice over the crispy pork and toss to combine before removing from the heat.
Toast the corn tortillas in a dry pan over medium heat until warm and slightly charred on the edges.
Assemble the tacos by filling the warm tortillas with crispy pork and topping with diced red onion, fresh cilantro, and sliced radishes.