1. Add chicken bouillon mixture to medium saucepan over medium-high heat; bring to boil. Add chicken; lower heat to medium. Simmer until chicken is cooked through, about 20 minutes. Transfer chicken to plate to cool; shred and set aside.
2. Meanwhile, heat oven to 180 degrees F; place baking sheet inside oven. Heat 1/2" oil in medium skillet over medium-high heat until shimmering, but not smoking. Add one tortilla; cook until crisp and golden brown on both sides, flipping once, about 1 minute. Transfer to paper towel-lined plate to drain, and then transfer to baking sheet in oven. Repeat with remaining tortillas.
3. To assemble tostadas, spread 3 tbsp. refried beans on each crisped tortilla. Divide reserved chicken, lettuce, tomato and avocado evenly among tortillas. Serve with salsita, pico de gallo, sour cream and cheese, if desired.