Add olive oil to Instant Pot and select the Sauté function.
Set to high and once the display reads “hot,” add red onion, bell peppers, and Poblano pepper.
Season with salt and black pepper, to taste, and cook, stirring continually, until the onion and peppers are crisp-tender and develop a bit of color, approximately 4-5 minutes.
Switch unit to “off” and transfer veggies to a separate bowl. Set aside.
Season chicken breasts on both sides with salt and black pepper, to taste.
Place chicken in Instant Pot, along with tomatoes, chicken broth, cumin, chili powder, Mexican oregano, and garlic powder. Stir to combine.
Add the lid and set the pressure valve to “sealing.” Select the “Manual” cooking option on the high setting and set cook time to 10 minutes. When done cooking, allow the pressure to release naturally for 10 minutes, and then do a quick release for any remaining pressure.
Remove lid and shred chicken breasts with two forks. Add sautéed veggies, black beans and lime juice. Stir to combine and taste.
Adjust seasonings as desired.
Allow soup to sit on “Warm” setting for several minutes until the veggies and beans are heated through.
Serve immediately topped with sliced avocados, red onion, Mexican cheese, and fresh cilantro, if desired.