Fighting a puppet master is either really easy or really difficult, depending on how well-trained they are. Generally, it all comes down to just outsmarting them. Most puppet masters I've faced are extremely vicious and relentless, just stay calm and think it through. They tend to favor one long range support and one short support. I usually make them waste their short range support, back up and use shuriken.
Each puppet master user is different in their style, they're fun to use but very difficult -- find the weakness and exploit it. Have fun!