No, Tanith wasn't stupid. She hadn't actually expected to hit him with the first shot. She had known he would dodge it, and would continue to do so for some time. Now that she had made up her mind to do this thing, she wasn't actually in any large hurry. She had plenty of bullets. If she continued to fire she could lead him for a while and eventually fake him out. In time he would do as she wanted. She'd fake to the left, and shoot right instead. This could continue for some time. She'd bleed him out if she had to, slow him down. When he was weakened, she could go for the finishing blow.
That was exactly what she aimed to do. When he moved, so did the gun. She would point at him again, and pull the trigger. Lather, rinse, repeat. He could take his time dying if he wanted to. But he would die. That was all that mattered.