Can someone tell me how long will a bad black eye last?

Days to weeks: A "black eye" is basically bruising of the soft tissues around the eye and face. There are tissue planes where hemorrhage can track, and blood often settles under the eyes, and sometimes can track across the nose to the other side. Nothing really makes this clear faster except time. Usually more will be gone within a week. Get an exam to check the eye to be sure no injury there, or to the orbit.

Week or two: A bad black eye, also known as ecchymosis, will resolve over time as your body breaks down the blood and carries it away. Icing the eye for the first two days to limit the swelling and bleeding can help. Applying heat from day four onward can bring more blood supply to the area and help to break down and carry away the old blood. It rarely will last more than a week or two.