You can always back track to the beginning of the mines and purchase blizzard magic off of the bangaa vendor. You'll get yourself a level or two and the magic and probably have a much easier time too.
Also, I never did this but I read in one of the guides on gamefaqs that if you run all the way to the north of the map when fighting the mimic queen there is an area you can get in where she won't be able to reach you with physical attacks.