Set the Instant Pot to the “Sauté (More)” setting. Once it is hot, add the vegetable oil.
Season the pork with 2 tablespoons kosher salt and 1 teaspoon pepper. Brown the pork shoulder in the Instant Pot, searing it on all sides. (If needed, do this in batches to avoid overcrowding the pot.)
Add all of the browned pork shoulder, plus any juices, to the Instant Pot.
Add the chopped onion, garlic, orange juice, lime juice, chili powder, oregano, cumin, coriander and chicken stock to the Instant Pot.
Set it on the “Pressure Cook” setting for 90 minutes and close the lid.
Once the pork is done cooking, transfer it to a cutting board and shred into larger, chunkier pieces using two forks.
Set the oven to BROIL and line a baking sheet with foil. Arrange the shredded pork in a single layer on the baking sheet and spoon a little of the braising liquid over the top. Broil 2 inches from the top of the oven on HIGH until crispy, 1 to 2 minutes. Watch closely.
Serve piled onto warm corn or flour tortillas and topped with Cherry Tomato Pico de Gallo.