First, prepare your workstation for frying the tortillas. Line a large baking sheet with paper towels and place a wire cooling rack on top. Then, preheat about a quarter-inch of vegetable oil in a large frying pan over medium to medium-high heat.
Once the oil is nice and hot, carefully place the tortillas in the pan with tongs (you will likely need to work in batches of only 2 or 3 tortillas at a time). Fry for about 30 seconds to 1 minute, until the bottoms are lightly golden brown, then flip and fry for another 30 seconds or so. Transfer tortillas to the wire rack to drain over the paper towels. Continue until all the tortillas have been fried.
Next, prepare your tostada toppings. If you have prepared shredded chicken tinga in the fridge, measure out about 1-1/2 cups in a microwave-safe dish. Reheat in the microwave for about 1 minute, stirring halfway through, or until warm. Similarly, transfer canned refried beans to a microwave-safe dish and heat for about 1 minute, stirring halfway through.
Next, scoop the avocado flesh into a small bowl and add the lime juice and sea salt. Mash with a fork until smooth, and set aside.
Finally, assemble the tostadas. First, spread a thin layer of refried beans over the top of each fried tortilla. Then, top with a spoonful of shredded chicken tinga and a scoop of mashed avocado. Finally, sprinkle with crumbled queso fresco and chopped cilantro. Serve immediately.