What is kojin jigyo?

Kojin Jigyo means self-proprietor.  It costs absolutely nothing to become one, and there are no fees associated with it. In fact most English schools in Japan are not KK (LTD.) but kojin jigyo. There is no limit to the amount of money you can make. You can become a kojin jigyo even while working full time at another place.

How would becoming a kojin jigyo benifit me?

Once you are a kojin jigyo you will have to fill out a Blue Tax sheet along with your regular white one. This doesn't sound very good...but it is! With the Blue sheet you can now write off anything related to your business.
Let's use private teaching as an example:

You teach privately at a coffee shop. Now you can write off your transportation, coffee, books, 25% of your rent for office space, telephone, and internet for communications etc. You will end up saving if not getting back money at tax time.

Is it difficult to become a kojin jigyo?

No, go to your tax office ask to become a kojin jigyo you will need to fill out one piece of paper hanko it and you are done. It takes longer to fill out a cell phone contract then a kojin jigyo.