Place the beef chunks into the inner pot of your Instant Pot.
Add the onion quarters, minced garlic, beef broth, apple cider vinegar, and lime juice to the pot.
In a small bowl, combine the chili powder, cumin, oregano, salt, pepper, minced chipotle peppers, and adobo sauce. Rub this spice mixture evenly over the beef chunks.
Tuck the bay leaves around the meat.
Secure the lid on the Instant Pot and set the vent to sealing.
Select the Manual or Pressure Cook setting and set the time for 60 minutes on High Pressure.
Once the cooking cycle finishes, allow the pressure to naturally release for 15 minutes before carefully switching the valve to quick release any remaining pressure.
Remove the beef chunks to a large bowl. Discard the bay leaves.
Use two forks to shred the beef thoroughly.
Skim any excess fat from the liquid remaining in the pot. Return the shredded beef to the pot and toss well with the cooking liquid until the meat is moist and coated with flavor.