here's my advice. If you truly want to come to japan, there are ways. please don't let people put you off with comments like "it's very difficult", "living here is not easy", "i would stay where you are", and more. a big chunk of the expat community in japan is here just out of passion and love for the country, not because they're making big bucks, and they adapt, and they're fine. Some of them eventually get to make good careers here, so that means you can also do it.
anyway, based on your profile, here are my comments.
do japanese companies hire only the best of the best from abroad? Not true, you don't have to be a genius or to have 3 phd's, just to meet the basic job requirements and have a decent resume. In your case, honestly, I think 1 year is too little, so companies are most likely to prefer local newly grads. Also, I don't see much of a chance doing a law job here, because well, you know that law is very relative to the country and requires different knowledge. Also, I honestly don't know but I would believe that law jobs require a very, very good command of japanese. Sure, you can learn, but it does take time to get to a level in which you can fully use it for work. People studying in Japan usually need about 2-3 years being full time students... so that gives you an idea.
Anyway, there are more options, but I would probably focus more on the arts degree. There's a lot of creative work done in Japan. I don't know what experience you have here, but what about targeting the marketing departments of international companies, for example? Another good, but less explored path are the internships. They're still not as common in Japan, but I can tell you that recently a lot of companies are opening internship programs and the requirements are much more relaxed. They are not well paid, you'll have to live in a sharehouse and budget your money, but it's only a step for you to find a full time position later. Make a list of companies that you're interested in and look for internships in their career websites.
The last resort is to become an english teacher, but if you must go this way, my recommendation is that you try to move out of it no later than one year or you run the risk of getting stuck and permanently damaging your career. Then no one will want to hire you for anything that is not for english teaching, not to say that at home your resume won't impress any employer. By the way, lots of singaporean english teachers here... schools many times will take even non-natives.
You also have the option to come here as a master degree student, but be aware that companies here don't put enough value on it, so they just see it as a 2-3 year gap in your resume. Stay too long there, and your only choice will be to continue with a phd and then maybe to become a research professor or something. if academics are your thing, then try to get a monbukagakusho.
anyway, just some ideas, hopefully one of them will fit you