In a bowl, combine achiote paste, orange juice, lime juice, minced garlic, cumin, oregano, salt, and black pepper. Whisk until smooth to create the marinade.

Place pork shoulder chunks in a large bowl and coat thoroughly with the achiote marinade. Cover and refrigerate for at least 2 hours or overnight for best results.

Prepare pickled onions by combining sliced red onions, white vinegar, sugar, dried oregano, and salt in a jar. Shake well and refrigerate for at least 1 hour.

Preheat oven to 150°C (300°F). Place marinated pork in a deep roasting pan with bay leaves and cover tightly with aluminum foil.

Roast pork for 3.5 to 4 hours until fork-tender and internal temperature reaches at least 75°C (165°F) for food safety.

Remove pork from oven and shred using two forks while still warm. Mix shredded meat with pan juices for extra moisture and flavor.

Warm corn tortillas in a dry skillet over medium heat for about 30 seconds per side until pliable.

Assemble tacos by placing generous portions of shredded cochinita pibil on warm tortillas. Top with drained pickled red onions, fresh cilantro, and sliced habanero if desired.

Serve immediately with extra pickled onions and lime wedges on the side.