Preheat the oven to 375°F (190°C).
In a medium bowl, combine the shredded chicken, olive oil, ground cumin, chili powder, garlic powder, onion powder, salt, and black pepper. Mix well to evenly coat the chicken with the spices.
Spread the seasoned chicken on a baking sheet and bake for 10 minutes until heated through.
While the chicken is baking, warm the refried beans in a small saucepan over low heat, stirring occasionally.
Place the tostada shells on a baking sheet and warm them in the oven for 5 minutes until crisp.
Remove the tostada shells from the oven. Spread about 2 tablespoons of refried beans evenly over each shell.
Top each tostada with an even layer of the seasoned shredded chicken.
Add shredded lettuce and diced tomatoes evenly over the chicken.
Sprinkle shredded cheddar cheese on top of each tostada.
Return the tostadas to the oven for 2-3 minutes to slightly melt the cheese.
Remove from the oven and drizzle about 1 tablespoon of sour cream over each tostada before serving.