Beating furhires with Amazoness can be an annoying process. I have done it once, but only by having a lot of stuff to protect myself. Basically, it came down to the opponent not having anymore ways to activate wiz once his hand was spent and me WODing him. Once his hand was emptied out of monsters to replace them, he couldn't recover. It was hard, though.
Amazoness is good for skilless player. But a skilled player have much better win rate.
Low ranked don't summon at battle phase or use Princess Combo to do OTK when they have a chance.
I haven't use Fur Hire yet, but played against it a few time. It have better chance in FH vs Amazoness. But not a 100%. (Amazoness must trick FH by set spell and trap tatically to have about 20-30% winrate).