Rub the pork shoulder thoroughly with sea salt, black pepper, ground cumin, dried oregano, and garlic powder.
Place the seasoned pork in a slow cooker and pour the fresh orange juice and lime juice over the top.
Cover and cook on low for 7-8 hours until the meat is tender and easily shreds with a fork.
Remove the pork from the slow cooker and shred it using two forks, discarding any large pieces of fat.
Heat the avocado oil in a large skillet over medium-high heat and add the shredded pork in a single layer.
Press down with a spatula and sear for 3-4 minutes until the bottom is golden and crispy, then toss and sear for another 2 minutes.
Warm the black beans in a small saucepan over low heat until heated through.
Briefly toast the corn tortillas in a dry pan until soft and slightly charred.
Assemble the tacos by layering the warm beans and crispy pork onto the toasted tortillas.
Top with diced red onion, fresh cilantro, and thinly sliced radishes before serving.