It is tough for sure since they are really good, but I did see someone beat fur hires with Amazoness once, so it can be done. What I should do is use more effect-killers for my deck.
Amazoness can beat fur hires. I have done it twice and an almost-win (very close) so far. If you can, it helps to use whatever is the least important trap/spell first in the hopes of saving the good ones for when they don't have enough to discard to use wiz's effect in a turn.