Greetings and welcome to JREF.
First, have a look at the Japanese Ministry of Justice homepage on visas
here. It sounds like you are after the cultural activities visa which is a general visa good for six months to one year.
The catch is, you cannot work on a cultural visa, and you will have to show that you have enough cash to support yourself for the length of your stay. You will not be allowed to work to "earn some money for general expenses."
I copied and pasted the following, again from the MOJ site. These rules are for general cases, but you can assume at this point all of them will apply to you.
1. In cases where the person concerned intends to engage in academic or artistic activities, or to engage in specific studies of Japanese culture or arts, the following materials are required.
Documents certifying the activity and its duration of the person concerned, and the outline of the organization where he or she intends to engage in the activity concerned.
Documents certifying the academic career, professional career, and other career regarding the activity of the person concerned.
Documents certifying that the person concerned can defray all expenses incurred during the stay in Japan.
2. In cases where the person concerned intends to learn Japanese culture or arts under the guidance of an expert, additional materials showing the career and the achievements of the expert, besides the documents mentioned above, are required
Of course the best thing to do is contact your local Japanese embassy or consulate and ask them directly.
Your certificate of elegibility will come from the martial arts teacher you will study with, so no problem there, but you will need to start saving some cash...
Good luck and enjoy the forum!