All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.
We ask Allah, the Exalted, to reward you generously for your keenness on asking about the religious rulings which you need to know and for adhering to the truth and righteousness. We ask Him to preserve for you your religiosity and bless you with steadfastness and success in your pursuit of useful knowledge and righteous deeds; verily, Allah (alone) is worthy (of this plead) and is Able to bring this to pass. Our advice to you is to supplicate Allah as much as you can and ask Him to grant you success.
Shaving the beard is prohibited, and it is impermissible to continue studying in this college that requires that the students shave their beards. You did well by trying to persuade the administration to reconsider this policy. If you believe that continuing your persuasive attempts might be effective, you should do so. You can also seek the help of some Islamic organizations of which you hope that they would be able to influence the administration in this regard.
If you succeed in convincing the administration, then that is the desired objective; otherwise, it is incumbent to look for another college where you are not required to commit this violation of the Shariah. It is impermissible for you to continue in this college unless you cannot find another college and you need to study this field. In this case, it would be acceptable to continue in it while obeying Allah to the best of your ability. If the administration allowed you to trim your beard instead of shaving it, it is impermissible for you to shave it because the need must be answered proportionately.
Allah knows best.