The Japanese authorities recognise BASI's Alpine, Snowboard, Nordic and Telemark qualifications.
Japan is not part of the EU, so a work permit is required to be able to work there. You can find out more about how to obtain one here.
It is also essential to obtain a prosecution history from the police to present with other paperwork. In the UK, this is available from www.disclosurescotland.co.uk (Scotland). This information must be no more than 3 months old but may take up to 6 weeks to obtain, so this should be obtained before arriving in Japan.