What visa do I need to work as an ALT?
Board postings most often name the Instructor (教育) status, or spouse or permanent resident status. Hirakata and Ginowan both list these.
Whether your own status fits is decided by the Immigration Services Agency of Japan, on the facts of each case. It depends on the role, on the employer, and on the person applying, and it is not something this site can determine.
The Immigration Services Agency publishes the current statuses of residence and the conditions attached to each. A certified administrative scrivener (行政書士) advises on individual cases.