1. Adjust oven racks to upper-middle and positions and heat oven to 425 degrees. Spread tortillas evenly in 2 rimmed baking sheets. Drizzle each sheet with 2 tablespoons oil, sprinkle with 1/4 teaspoon salt, and toss until evenly coated. Bake, stirring occasionally, until tortillas are golden brown and crisp, 15 to 20 minutes, switching and rotating sheets halfway through baking.
2. Toast guajillos in 12-inch cast-iron skillet over medium heat, stirring frequently, until fragrant, 2 to 6 minutes. Transfer toasted guajillos to blender and process until finely ground, 60 to 90 seconds. Add tomatoes and their juice, 3/4 cup onion, poblano, jalapeño, garlic, cilantro sprigs, and 3/4 teaspoon salt to blender and process until very smooth, 60 to 90 seconds.
3. Pound thicker ends of chicken breasts as needed to create even thickness. Combine guajillo-tomato mixture and broth in now-empty skillet and bring to simmer over medium-high heat. Nestle chicken into sauce. Reduce heat to gentle simmer, cover, and cook until chicken registers 160 degrees, 10 to 15 minutes, flipping chicken halfway through cooking.
4. Transfer chicken to carving board, let cool slightly, then shred into bite-size pieces using 2 forks. Meanwhile, increase heat to medium and simmer sauce until thickened and measures 4 cups, about 6 minutes.
5. Stir shredded chicken into sauce and cook until heated through, about 2 minutes. Off heat, stir in tortillas, cover, and let sit until tortillas have softened slightly, 2 to 5 minutes. Sprinkle with queso fresco, avocado, radishes, remaining 1/4 cup onion, and minced cilantro. Serve immediately.