Combine chicken thighs, bell pepper, tomato, and green chiles in your Instant Pot.
Pour in chicken broth and tomato sauce. Sprinkle with chili powder, ground cumin, chipotle powder, smoked paprika, and garlic powder. Season with salt and black pepper, then stir everything together gently.
Secure the lid on your Instant Pot, making sure the pressure valve is set to "Sealing." Select the "Manual" setting on high pressure and set the cooking time for 10 minutes.
Once cooking is complete, let the pressure release naturally for 10 minutes. After that, carefully do a quick release for any remaining steam.
Open the lid and carefully take out the chicken thighs, placing them on a plate. Use two forks to shred the chicken, then return it to the pot.
Gradually stir in the Mexican cheese, a little at a time, to ensure it melts smoothly without clumping. Then, add the chopped cilantro and stir until the cheese is fully melted.
To serve, ladle the delicious soup into bowls. Garnish with a sprinkle of fresh cilantro, some extra Mexican cheese, and avocado chunks. Serve immediately with lime wedges for a fresh squeeze, if you like. Enjoy your easy, healthy meal!