Not f2p, but if you have edo Deidara it works quite well. Jiraiya will surpress immunity and prevent Shizune/Karin from healing. Deidara finishes the job next round before they do anything.

I think most ninjas will do well, you just need some kind of control in chase (blind, ignition, immobile, chaos), so Shizune and Karin don't heal after Jiraiya's mystery hits. Necessary control can be provided by Fire Main's 1st, 2nd or 4th chase :)