For most of the series, she does not wear a hat. It is only after she becomes Hokage that she wears the Hokage hat. This is a great way to make the Tsunade costume more recognizable, as she is the only female Hokkage in the show, so it is hard to mistake her for someone else. You can easily make this hat yourself by painting a classic Chinese straw hat white and then adding red kanji on the front with paint.