Whisk beer, teriyaki sauce, chili powder, and garlic powder together in a bowl; pour into a resealable plastic bag. Add the chicken, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator 6 to 24 hours.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken from the marinade and shake off excess. Discard the remaining marinade.
Cook the chicken breasts on preheated grill until no longer pink in the center and the juices run clear, 7 to 10 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Arrange chicken breasts in a baking dish and top each with a slice of Muenster cheese.
Preheat oven to 350 degrees F (175 degrees C).
Combine tomatillos and water in a large saucepan; bring water to a boil, place cover on saucepan, reduce heat to medium-low, and cook until tomatillos begin to burst, 7 to 10 minutes. Stir onion and garlic into tomatillo sauce; season with salt and pepper; continue cooking at a low boil until onion is tender, about 15 minutes.
Pour tomatillo sauce into a blender. Cover and hold lid down; pulse a few times before leaving on to blend until smooth. Stir sour cream and cilantro into the tomatillo sauce; pour over the chicken and Muenster cheese.
Bake in preheated oven until cheese melts, about 15 minutes.