In a small bowl, combine the salt, pepper, cumin, oregano, paprika, and garlic powder. Season both sides of the chicken with this seasoning mix.
Turn the Instant Pot on the sauté function and heat the oil. Working in batches, sear the chicken until golden brown on both sides, 2 to 3 minutes per side. Set browned chicken aside and continue cooking until all chicken is browned, adding additional oil if your Instant Pot runs dry.
Add the chipotle peppers and tomato paste. Stir to toast the paste, about 1 minute. Add the green chiles and beer and whisk to combine.
Nestle the chicken back into the Instant Pot and turn the sauté function off. Securely fasten the lid on top of the Instant Pot, making sure the vent is sealed. Select the “manual” or high pressure setting and set the time to 15 minutes.
When the cook time is complete, release the pressure manually by carefully turning the valve. When all of the pressure has been released, remove the lid and transfer the chicken to a rimmed baking sheet (do not discard the remaining liquid in the Instant Pot). Using two forks, shred the chicken, then add back to the Instant Pot.