The complete Latin III National Latin Exam study guide can be found here. You can easily find online any information about culture, history, mythology, or geography that you do not know.
This exam has been redone recently to be almost exclusively reading comprehension questions, so I recommend you practice by taking the reading comprehension portions of the old Latin III NLE's found here. For explicit grammar practice, the online practice app for the NLE can be found here.
All grammar that we have not yet covered is described briefly in the document below: