Season the pork shoulder chunks with salt, black pepper, cumin, oregano, and chili powder, pressing the spices into the meat.
Set the Instant Pot to saute mode and add the olive oil. Once hot, sear the pork in batches until deeply browned on at least two sides, about 3 minutes per side. Remove and set aside.
Add the quartered onion and smashed garlic to the pot and cook for 2 minutes. Add the chopped chipotle peppers and adobo sauce, stirring for 30 seconds.
Pour in the orange juice and lime juice, scraping the bottom to deglaze any browned bits.
Return the pork to the pot and toss in the bay leaves. Lock the lid and set the valve to sealing. Pressure cook on high for 45 minutes.
Allow a natural pressure release for 15 minutes, then carefully switch the valve to venting. Remove the lid once the pin drops. Discard the bay leaves and onion quarters.
Transfer the pork to a large bowl and shred it with two forks. Ladle about 1/2 cup of the cooking liquid over the shredded pork and toss to keep it moist.
For crispy carnitas, spread the shredded pork on a lined baking sheet in a single layer. Broil on high for 4 to 5 minutes until the edges are golden and crispy.
Serve the carnitas on warm corn tortillas topped with fresh cilantro, diced white onion, and a squeeze of lime.