Add the chicken breasts, chicken broth, black beans, diced tomatoes, Rotel, chili powder, cumin, oregano, salt, and pepper to the Instant Pot liner. Do not stir excessively.
Secure the lid and set the valve to Sealing. Cook on Manual/Pressure Cook setting on High Pressure for 10 minutes.
When the cooking cycle finishes, allow the pressure to naturally release for 5 minutes, then carefully quick release any remaining pressure.
Remove the chicken breasts to a cutting board and shred them using two forks. Return the shredded chicken to the soup.
Stir in the fresh lime juice. Taste the soup and adjust salt and pepper if needed.
Ladle the soup into bowls and top with your desired garnishes like tortilla strips, cheese, avocado, and cilantro.