Preheat the oven to 350 F. In the bowl of an Instant Pot or pressure cooker, add the chicken breasts. Top with 1 can of enchilada sauce, the diced onion, and both cans of green chiles.
Close the top of the Instant Pot and seal the pressure valve. Pressure cook on high for 13 minutes. Allow to naturally release.
Remove the chicken breasts and place in a stand mixer to shred. Once shredded, add the chicken back into the sauce mixture remaining in the Instant Pot. Stir well.
Pour half of the remaining can of enchilada sauce into the bottom of the baking dish.
Start assembling the enchiladas, by scooping a portion of the chicken and chile mixture into a flour tortilla. Top with a few tablespoons of shredded cheese. Then, roll up the enchilada leaving the ends open. Place enchilada seam side down in a large baking dish. Repeat with all remaining tortillas and chicken mixture.
Once all enchiladas have been added to the baking dish, top with remaining half can of enchilada sauce. Then top with 1 cup of shredded Mexican cheese.
Bake in the preheated oven for 15-20 minutes, until the cheese is melted and tortillas are starting to get golden brown.
Remove the enchiladas from the oven and serve with optional toppings of cilantro, avocado, and sour cream.