This should give you a basic idea of how much essential things cost:
Cost living in Tokyo - cost of living in Japan
To give you another perspective, Tokyo is one of the costliest cities to live in - definitely among top 10, as per wikipedia and youe monthly budget is ~1000 USD. So I'd think it's going to be tight. Even if you share apartment, rent and cost of traveling is quite high.
It may be a bit easier if you choose a different city in Japan.