Heat the vegetable oil in a large skillet over medium-high heat. Add half of the tortillas and cook, turning with tongs, until golden, about 3 minutes; drain on paper towels. Repeat with the remaining tortillas. Reduce the heat to medium and add the zucchini; cook, stirring occasionally, until crisp-tender, about 2 minutes. Stir in the chicken, tomatillo salsa, 3/4 cup water and the cilantro; bring to a simmer and cook 2 minutes. Meanwhile, preheat the broiler. Spread half of the fried tortillas in an 8-inch-square flameproof baking dish. Top with about half of the chicken mixture and 1/2 cup cheese. Cover with the remaining tortillas, then the remaining chicken mixture and cheese. Broil until the cheese is melted, 2 to 3 minutes. Serve topped with radishes, red onion and cilantro.