Heat the olive oil in an Instant Pot set to sauté high.
Add the ground chicken, pressing it into an even layer at the bottom of the pot. Let it sear for 5 minutes without stirring.
After 5 minutes, add salt, black pepper, garlic, cumin, and chili powder. Break the chicken into crumbles, ensuring the spices are evenly distributed.
Remove the chicken with a slotted spoon and set it aside.
While the Instant Pot remains on sauté mode, add the onion, jalapeño, and serrano peppers. Lightly season with salt (about ½ teaspoon). Cook until the vegetables soften, about 3 minutes.
Turn off the Instant Pot.
Add the Hatch green chilies with their liquid, drained and rinsed hominy, drained beans, beer, Mexican oregano, bay leaf, and baking soda. Stir well to combine. Scraping the bottom of the instant pot to get any of the golden brown bits off and incorporated into the stew.
Set the Instant Pot to pressure cook - high pressure and cook for 8 minutes.
Allow the pressure to release naturally for 10 minutes, then quick-release any remaining pressure.
Remove the lid and stir in the cilantro and lime juice.
Taste and adjust salt and pepper as desired.