Preheat the oven to 350 degrees F. Sprinkle the taco seasoning and chili powder all over the chicken breasts.
Heat the oil in a nonstick skillet over medium-high heat. Add the chicken and saute on both sides until browned, about 5 minutes per side, then remove from the skillet and set aside. To the skillet, add the tomato sauce, hot sauce and 2 cups hot water and bring to a gentle boil.
Shred the chicken with 2 forks, then return the shredded chicken to the liquid and simmer on low until everything is hot and bubbly.
Assemble the nachos in 2 ways: Sprinkle a layer of tortilla chips onto 2 ovenproof plates or baking dishes. Sprinkle both with cheese and then a layer of chicken; repeat twice more with each layer getting smaller in circumference. Finish with an extra sprinkling of cheese. Bake just until the cheese melts, 5 to 10 minutes.
Serve one dish as is. On the other, layer on the jalapenos, black olives, tomatoes, green onions and sour cream.