Cook chicken by simmering in an uncovered pan of water for about 20 minutes. Using a slotted spoon, transfer chicken to a rack to cool. Shred the meat and set aside.
Heat 1 tbsp (15 mL) oil in a large frying pan over medium-high heat. Add peppers, onions, and garlic. Sauté until softened, about 8 minutes. Stir in chili powder, paprika, cumin, pepper, and salt; cook 2 minutes more. Stir in tomatoes and sugar. Simmer, uncovered, until sauce thickens, about 8 minutes. Remove from heat; keep warm. Meanwhile, in a saucepan, heat beans over medium heat in their liquid; drain and rinse.
In a heavy frying pan (cast iron), heat the remaining oil and toast tortillas, one at a time, over high heat, until crisp and lightly browned, about 1 minute per side. Keep warm.
To assemble, divide chicken, tomato sauce, beans, diced tomato, and lettuce among all 8 tostadas. Sprinkle with jalapeños. Top with 1 tbsp (15 mL) each of the cheddar cheese and sour cream, plus a radish slice and some salsa, if desired.
Per tostada: 329 calories, 32 g protein, 8 g total fat, 1 g saturated fat, 67 mg cholesterol, 34 g carbohydrates, 8 g fibre.