You can have 7 ninjas in your team- and use 3+ main for a lineup- this gives you 3 free spots for ninjas you can save for other rounds- choose ones that will be doing dmg for puppets in next rounds (take note of what type those are) and before round you can choose "lineup" option, next to start and set other ninjas from those 7 you choose to team.

It's good to have GNW TenTen as she is doing dmg of all the natures- so all puppets will get hit from her mystery. They are also not immune for ignition and poison- this will help you to finish them off.

Take note of what type of puppets there are and check ninjas that have certain type of nature dmg not only Tai or Nin in description of their skills.