Take your best shot means try your best, even if you think you wont be able to do very well or you think you might lose just have a go and you might do well but you wont know if you don't try.
Not a chance means that he will not do it and you can not make him do it as he does not want to or he can not do it. e.g. "Do you think I could pass for 21, "Not a chance".
