Don't know if you actually beat it yet by now, but now that is embarrassing, playing through the game again myself now and just beat that slime boss now, and you actually have to get rid of the girls first to stop the insane healing, Jupirirs sandrun skill is effective against the girls(not sure what attack type that skill is, so dunno if there are other skills on other monsters that can be used too) a handfull of rounds and it should get rid of the girls and after that you can kill the slime boss itself, as you said fire good for that, but really not critical anymore since there will be no healing. Also make sure not to have eliza knocked down, since it can heal for about 1k by raping her as well, it doesn't seem to be knocking her down herself though, just keep that in mind to make sure to use eliza relief, if you do want some ehmm.. rapebuffs(?).
(and yeah I geuss that means jupiri is needed for this fight, actually been playing without using jupiri and pukis so far, as tbh both of them are a bit too good compared to everything else, but had to get jupiriri onboard for this fight)