As an international students in Taiwan, you have to have the authorization to stay & work in Taiwan.
You would need to apply for the visa before entering Taiwan and apply for the ARC after entering Taiwan within particular period.
Since your purpose for stay is "studying", you would need to apply for the working permit if you want to work part-time. You would also need to apply for "job searching ARC" once you graduate if you wish to stay in Taiwan.
More information & steps: