Prepare the Mango Salsa: In a medium bowl, combine diced mango, chopped tomatoes, avocado pieces, red onion, jalapeño, and cilantro. Squeeze the juice of half a lime over the mixture and sprinkle with salt. Gently toss everything to combine well. Cover and place the salsa in the refrigerator to chill while you prepare the rest of the meal.
Season and Cook the Chicken: Sprinkle the taco seasoning evenly over both sides of each chicken cutlet. Pat the seasoning gently into the meat with your hands to ensure it adheres well. Heat the vegetable oil in a large skillet over medium-high heat. Once hot, carefully add the chicken pieces to the pan. Cook without moving them for about 3 to 4 minutes until the underside forms a nice golden-brown crust. Flip the chicken and cook the other side for another 3 to 4 minutes, until fully cooked through. Remove the chicken from the skillet, place on a cutting board, and squeeze the juice of the remaining half lime over the top. Let the chicken rest for 5 minutes to retain its juices.
Warm the Black Beans and Toast Tortillas: While the chicken rests, transfer the black beans to a small saucepan. Heat them gently over low heat, stirring occasionally until warmed through. At the same time, heat a nonstick skillet over medium-high heat. Lightly toast each tortilla for 30 to 60 seconds per side until they become warm and slightly crisp. Stack the tortillas in a tortilla warmer or wrap them in foil to keep warm.
Assemble the Tacos: Slice the rested chicken into thin strips suitable for filling tortillas. To assemble, place a small spoonful of warm black beans onto each tortilla, add several chicken strips, then top with a generous scoop of the mango salsa. Add shredded cabbage, sour cream, and cheese as desired to complete your tacos.