I just can't kill the professor. I don't have alzures shield and the professor does. I even found a way to get to the professor without being attacked by anyone so there are only kikimores attacking me during the fight.

He dodges all strong steel attacks and even most of my fast steel ones.

I know I can just load an earlier save at the inn to better prepare myself but it still seems hopeless based on the ease of which the professor and the kikimores kill me.

Do you have any advice or should I just grind for a while because I'm level 20 right now.

The professor should not have alzur`s shield only Geralt should have that as evidenced by the electrical field that surrounds him . Might try signs like Aard or Igni . Also oils like Hanged Mans Venom or maybe use a whetstone that gives 20% extra damage . Could also apply a temporary rune to your steel blade if you have any in your inventory .