Hmm, I haven't encountered this type of player yet, but I have a couple of thoughts. Depending on the map you're playing, you may be able to disrupt them by powering up your monks. Granted, getting a skull will be tricky, but some maps have skulls placed in them at the start.
1) Use a salamander to get just close enough to summon an Oni or two, then back off. That should at least soften them up, and hopefully give you an opening to go in. Or perhaps you can keep doing this over and over to wear them down, or use it to take the brunt of the attack and use your archers to help cleanup.
2) If you can get 3 skulls (which might be *very* hard), use a demon crow or salamander's most advanced spells to do damage multiple units. This takes 100 rice so can't be used a lot, but may disrupt their strategy if they are just healing up individual units to prevent any of them from dying.
It's tricky. You've probably tried carefully positioning, but you may be able to get the upper hand by approaching with a couple infantry and archers, take a couple miss-range shots with your archers and then retreat. You should be able to take out an enemy infantry, of course the same may happen to you on the next turn, but you may be able to use some nearby rocks or bamboo to your advantage. Perhaps if you know you'll lose a unit, you can position it such that the skull it leaves will draw them out a little?
Finally, you might be able to use the crow to gust an Oni in close, or one of your powered up units (if you've managed to grab any skulls).
Good luck! I'd love to hear any other ideas, as well as how it goes... death to the turtles!