If your visa, for example a Bridging Visa, has a no work condition attached to it, it may be possible to apply for work rights if you can satisfy the Department of Immigration and Border Protection (DIBP) that you have a “compelling need to work” and you (and any dependant family members) will suffer “financial hardship” if you are not permitted to work.
The DIBP will take into account evidence of your current financial situation and your day to day expenses in assessing whether you have a compelling need to work. This is not just a matter of filling out an application form and giving the DIBP information about your financial situation. Your savings, income and expenses must be backed up by verifiable evidence.