Preheat the oven to 375°F (190°C).
In a large bowl, combine the cooked shredded chicken, salsa, black beans, corn, and taco seasoning mix. Stir well to evenly coat the chicken and vegetables with the seasoning.
Add the sour cream, 1 cup of shredded cheddar cheese, 1/2 cup of shredded Monterey Jack cheese, chopped green onions, and chopped cilantro to the chicken mixture. Mix until well combined.
Lightly spray a 9×13-inch casserole dish with cooking spray.
Spread half of the crushed tortilla chips evenly on the bottom of the casserole dish.
Pour the chicken mixture over the layer of tortilla chips and spread evenly.
Sprinkle the remaining crushed tortilla chips over the top of the chicken mixture.
Top with the remaining 1 cup shredded cheddar cheese and 1/2 cup shredded Monterey Jack cheese.
Cover the casserole dish tightly with aluminum foil and refrigerate if making ahead. The casserole can be refrigerated for up to 24 hours before baking.
When ready to bake, remove the casserole from the refrigerator and let it sit at room temperature for 15 minutes.
Bake the casserole covered with foil for 20 minutes.
Remove the foil and bake for an additional 10 minutes, or until the cheese is melted and bubbly and the casserole is heated through.
Remove from the oven and let cool for 5 minutes before serving.