Season the Pork: Generously season the pork cuts with adobo seasoning and extra black pepper, or simply with salt and pepper, making sure each piece is thoroughly coated.
Heat the Oil: In a large stainless steel pot, melt the oil or lard over medium-high heat. Once hot, add the pork and fry until well browned on all sides.
Add Garlic: After the meat is seared, add the smashed garlic cloves. Stir occasionally to prevent sticking or burning. Though the carnitas aren't fully cooked at this point, you'll notice the color beginning to change. If using pork skin, add it now.
Add Liquids: Pour in the beer, along with the orange and lemon zest, orange juice, and lemon juice.
Cook: Bring the mixture to a boil, then reduce the heat to a simmer. Cover and cook for about 1½ hours until the pork is tender.
Caramelize: Uncover and continue cooking until the liquid reduces completely and the meat starts caramelizing, about 1 more hour. The pork will cook slowly in its own fat and juices, caramelizing as the liquid evaporates.
Drain: Once the carnitas are caramelized, remove them from the pot and drain off any excess fat using a colander.
Serve: Transfer the pork to a cutting board, shred it, and serve with warm corn tortillas (charred over a flame). Offer toppings on the side, such as salsa verde, diced onions, cilantro, radishes, lime wedges, and avocado.