Heat the oil in a pressure cooker over medium-high heat. Season the pork with salt and pepper, then brown it in the hot oil, stirring occasionally, until evenly browned, about 15 minutes.

Meanwhile, blend the orange juice with the chiles, vinegar, garlic, achiote paste, and salt until smooth. Pour this mixture over the browned pork. Cover the pressure cooker and reduce the heat once the valve starts to sound. Cook for 45 minutes.

Turn off the heat and let the pressure release naturally. Transfer the pork to a bowl and reserve the cooking juices in the pot. Shred the pork and pour the reserved juices over the meat.

To make the salsa, combine the onion with the chiles and lime juice. Season with salt and let it sit, stirring occasionally, while the pork cooks.