In a large pot, add the chicken breasts and cover with water. Bring to a boil over medium-high heat. Once boiling, lower the heat and let them simmer for 15 minutes, or until cooked through. Remove the chicken from the pot and shred it with two forks. Set aside.
In the same pot, add a splash of oil and sauté the diced onion over medium heat for about 5 minutes, or until translucent. Add the minced garlic and cook for an additional 1 minute.
To the pot, add the shredded chicken, black beans, corn, diced tomatoes with green chilies, chicken broth, chili powder, cumin, paprika, salt, and pepper. Stir well to combine.
Bring the mixture to a simmer and cook for about 10 minutes, allowing the flavors to meld together.
Stir in the heavy cream and let the soup heat through for another 5 minutes. Adjust seasoning with more salt and pepper if needed.
To serve, ladle the soup into bowls, and top each serving with tortilla strips, shredded cheese, fresh cilantro, and a squeeze of lime if desired.