(eg. Engineering, commerce/accounting, law, architecture, etc.)
And if so, what level of Japanese proficiency is required?
It seems that the majority of foreigners I meet in Japan work as English teachers, and to do this little to no experience or qualifications are needed in any discipline. But I believe that foreigners are sought after in other fields too. I often hear of international companies sending their employees to Japan. However, these people have usually already proven themselves to their own branches of their companies...
I suppose my question is: is it difficult for us to apply to these types of Japanese companies directly, having only just graduated from university?
(Personally, I'm interested in engineering, as I just graduated in that discipline last year. I'm currently working as an ALT in order to pick up more of the language, but after this I'm very interested in working here in my own profession. I would say my Japanese is at an intermediate level, but I've never taken the JLPT.)