In a bowl, combine the achiote paste with the orange juice, lime juice, vinegar, crushed garlic, salt, pepper, and oregano to create a flavorful marinade.
Rub the pork shoulder with the marinade, then let it rest for at least 4 hours, or preferably marinate overnight.
Preheat the oven to 320°F (160°C). If using banana leaves, line a baking dish with them, then place the meat inside and cover with aluminum foil.
Bake the meat for 4 hours, or until it is completely tender and easily shredded.
Remove the meat from the oven, then use two forks to shred it.
Warm the tortillas in a skillet or directly over a flame until lightly charred.
Fill the tortillas with the Cochinita Pibil meat, then sprinkle with finely chopped red onion, cilantro, and chili.
Squeeze fresh lime juice over the top before serving for an even more intense flavor.
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