Jobs in finance can be with Japanese firms, where you are very likely to need spoken and written Japanese skills, or with foreign firms that have branch offices here. In the latter case, you may or may not need as much Japanese. Case by case. Makes sense to know as much as possible, though, doesn't it?
Chidoriashi stated it correctly. You start at the bottom rung (level 4) and work your way up to level 1, but how long it takes will depend on you. The test is held only once a year, and you can choose to skip levels if you like. But, learning is a personal thing. Self-study outside Japan will be harder than in Japan, obviously. Book learning vs. real-life language usage is also something to consider. I'd say Chidoriashi's estimate of 5 years from scratch to level 1 is pretty close, but it all depends on your circumstances.
If there is no description for a Japanese language requirement in the job ad, it could mean anything -- they forgot to fill it out, they didn't care what level, they cared but still want to see who applies, etc. At least it's a more hopeful sign than seeing a number you can't yet achieve!
EDIT: I just looked at the site to see what you ran across. One example was for an unnamed company, but since the ad was entirely in Japanese, you will have to use common sense to figure that applicants will need a pretty high level of Japanese.
CEO's hired from abroad are more likely NOT to need as much Japanese, but I suspect that at this stage in your life, you are not going to be shooting for such positions right now.
FYI: Intracompany transfers will provide their own visa type, but you have to work for the company for a year first. So, if you get in with a company in your home country and expect a transfer, remember that. Also, newbies (especially in the lower ranks) are not likely to be sent overseas right away anyway).