In a small bowl, combine the salt, pepper, cumin, oregano, paprika, and garlic powder. Stir until well incorporated. Season both sides of the chicken with this seasoning mix.
Turn the Instant Pot on the sauté function and heat the oil. When hot, in batches to not overcrowd the Instant Pot, 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.
Next, add the chipotle pepper and tomato paste. Stir to toast the paste, about 1 minute. Add the green chiles and beer to the Instant Pot and whisk to combine.
Nestle the chicken back into the Instant Pot and turn the saute function off. Securely fasten the lid on top of the Instant Pot, making sure the vent is sealed. Press the "manual" and then set the time to 15 minutes. Walk away from the Instant Pot and let it do its thing! Note: If your IP doesn't have a manual button, set it to 'high pressure.’
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 IP). Using two forks, shred the chicken then add back to the Instant Pot.