I haven't seen any strategy threads for this mission on MB. So, here is the team that I used.
Round 1: Use your main's ability on the Taijutsu puppet. Then hope Kankuro's puppet is alive in round two.
Round 2: Kankuro's mystery or just hit the ninjustu puppet with standards.
Round 3: Use Tenten on the fire puppet. It should pretty much kill it.
Round 4+: Just use mysteries to finish off what you have left.

Might be better to set the formation to:
GNW Kank Puppet Main
Jiko Tenten Main Puppet
X X X