Add chicken, onion, garlic, beans, corn, green chiles, chili powder, cumin, oregano, cayenne pepper, salt, and chicken broth to Instant Pot.
Close lid on Instant Pot and seal pressure valve.
Cook on HIGH pressure for 20 minutes.
After the 20 minutes of cooking, let the pressure naturally release for 10 minutes, and then release the rest manually.
Remove the chicken breasts from the soup and shred with two forks. Return to the pot.
Transfer 1 cup of the liquid to a bowl. Stir in the Greek yogurt until smooth.
Pour broth/yogurt mixture back into the Instant Pot, stirring well.
Add the cheese, stirring until melted. The heat from the soup should melt it, but you can also turn the saute function on to speed up this step. Be sure to stir continuously, so the bottom does not burn if you turn saute function on.
Serve topped with a dollop of Greek yogurt, diced green onions, shredded cheese, and sliced avocado.