Begin by marinating the chicken. In a bowl, combine the achiote paste, bitter orange juice, lime juice, ground cumin, and minced garlic. Mix well. Place the chicken breast fillets in the marinade, ensuring they are evenly coated. Let them marinate for at least 30 minutes, or preferably overnight in the refrigerator.
Once the chicken has marinated, prepare the sauce. Turn on the Instant Pot's sauté function and heat the oil. Add the diced onion, minced garlic, diced tomatoes, and diced red bell pepper. Sauté the vegetables until they are softened, about 5-7 minutes.
Once softened, remove the vegetables from the Instant Pot. Blend the vegetables or grind them with a food processor. If you wish, you can add one or two guajillo chiles. Reserve.
In the same Instant Pot, using the sauté function, add the marinated chicken breast fillets. Sauté them for about 2-3 minutes on each side until they are lightly browned. This step helps to seal in the flavors.
After sautéing the chicken, remove it from the Instant Pot and set it aside. Take a large piece of aluminum foil and place it on a flat surface. Place the sautéed chicken breast fillets on the foil. Pour any remaining marinade over the chicken, then spoon the juice of sautéed vegetables on top of the chicken.
Carefully seal the aluminum foil to create a packet, ensuring that none of the juices can escape. Place the foil packet on the steaming rack of the Instant Pot.
Add water to the Instant Pot according to manufacturer's instructions for steaming.
Close the Instant Pot lid and set the valve to the sealing position. Cook on high pressure using the steam function for 20 minutes.
Once the cooking time is complete, allow the pressure to release naturally for 5 minutes, then do a quick release of any remaining pressure.
Carefully open the foil packet, being mindful of the steam. Use two forks to shred the chicken directly in the packet, mixing it with the vegetables and juices.
Serve the Chicken Pibil hot, either on its own or accompanied by vegetables, tortillas, or your favorite side dishes.