Rub the pork shoulder evenly with the ground cumin, dried oregano, sea salt, and black pepper.
Place the seasoned pork into a slow cooker along with the minced garlic, orange juice, and lime juice.
Cover and cook on low for 8 hours or high for 4 hours until the meat is tender and shreds easily with a fork.
Preheat your oven broiler to high and line a baking sheet with parchment paper.
Shred the cooked pork using two forks and spread it in a single layer on the prepared baking sheet.
Broil the shredded pork for 3 to 5 minutes until the edges become golden and slightly crispy.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side until soft and pliable.
Divide the crispy carnitas between the tortillas and top with sliced avocado, thinly sliced radishes, chopped cilantro, and finely diced red onion.