Yes, it is difficult, did you expect it to be otherwise? The non-EU hiring rules are strict and unless there are few Swiss/EU candidates to fill the position you're not going to be hired. https://www.bfm.admin.ch/bfm/en/home...zulassung.html
The good news is that foreign students who graduate from a Swiss uni are supposed to be on equal footting when it comes to being hired. But an employer still needs to prove an economic or scientific importance criteria to be able to hire you. https://www.bfm.admin.ch/bfm/en/home...abgaenger.html
I don't know your field, but I would think that a law degree isn't going to be especially economic or scientific to meet the criteria.
That said, you do have an employer who's interested in hiring you so you may be chosen and they will then apply for a permit. If your combination of skills are the only fit for the position then they stand a good chance of getting approval.