Qualifications..... well, knowing somebody that knows somebody might get you in, and saying that mostly because the language barrier could likely be a big handicap in trying to get someone to take you on. Given that you could initially get around that somehow, a proven capacity to do the work might alleviate a lot of the language inconveniences for both sides, plus you'd be learning the lingo that applies to what you are doing.
If I was coming over to Japan with the intent of doing tree work, I'd want to stay in the big cities, especially Tokyo or maybe Osaka. Big city may not be your preferred environment, the traffic is a living hell, but the diversity of work there is much expanded, as you can imagine in an ancient place with a lot of narrow streets, where mechanical equipment often can't get in. Also, there are more people doing it, so better opportunities in that regard.
Last and maybe not least, there can be a huge quantity of other things of great interest for a young man in the cities.
Out in the countryside, it tends to be more old boy, and work is way down, given the economy. Nice if you could get connected to a good outfit in a more rural and attractive place, but such opportunities are rather limited, imo.
Hope this might help.