Heat vegetable oil; working in two batches, add pork and cook until evenly browned, about 3-4 minutes.
Stir in beer, orange juice, lime juice, garlic, oregano, chili powder, cumin, salt and pepper. Select manual setting; adjust pressure to high, and set time for 30 minutes. When finished cooking, quick-release pressure according to manufacturer’s directions.
Remove pork shoulder from the Instant Pot® and shred the meat using two forks; season with salt and pepper, to taste, if needed.
Preheat oven to broil. Place pork onto a baking sheet and broil until crisp and crusted, about 2-3 minutes.