You could try applying at one of the big TV networks like NHK. Of course, you'd have to know Japanese:
NHK
I've got 2 roomates in the industry (one's a director, the other's a producer). But they're both Japanese, went to film school here, and have 20 years of experience. Not sure how a new grad would get into the industry, especially one from outside of the country. I did hear stories that one of my roomates (the producer) started out as part of a film crew (camera man). I'm guessing there's some kind of apprenticeship type of path you'd have to go through to do the same. It does seem a bit improbable that you'd get visa sponsorship as an apprentice though.
My other roomate (the director) freelances. It would take quite a bit of networking to do something similar. Plus, with freelancing you don't have a company than can sponsor your visa. Of course if you've somehow gotten a company to sponsor your visa before you go the freelancing route and can prove that you can and have been supporting yourself financially, you could later get a self sponsored visa after a couple of years (*possibly*...check the TokyoCooney video where he talks about visas).
YouTube - F.Y.I. Tokyo: Visas
I dunno. Seems like a tough field to get into from abroad. Good luck with your quest.
Actually, your best bet would be to learn as much as you can from TokyoCooney. He seems to be the one person closest to your line of work that I can think of. See how he got into Japan and pursued work in the entertainment industry.
http://www.tokyocooney.com