Warm 1/4 cup of olive oil in a skillet over medium-high heat. Slice the corn tortillas into thin strips and fry them in small batches until they are golden and crisp. Transfer them to a paper towel-lined surface to remove excess oil. Continue until all strips are fried, supplementing with additional oil if necessary. Set aside.

In a large pot, heat the olive oil over medium-high heat. Add the chopped onion, minced garlic, and diced jalapeño. Sauté until the vegetables become tender and aromatic. Incorporate the whole chicken breasts, crushed tomatoes, black beans, corn, cumin, chili powder, salt, chicken broth, and 1/4 cup of the chopped cilantro. Bring the mixture to a boil, then reduce the heat and let it simmer for 25 minutes. Remove the chicken, shred it using two forks, and return it to the soup. Simmer for an additional 5 minutes, then stir in the lime juice.

Ladle the soup into bowls and top with crispy tortilla strips, diced avocado, a sprinkle of the reserved cilantro, and lime wedges on the side.