Yep, death is a really annoying status effect. I don't recall which boss that was precisely, but I do recall having a couple of fights with it.
There are several ways of avoiding this.
First, take lots of resurrection items with you.I forget exactly which item restores at which shop, but they shouldn't be too hard to find. Since usually only one puppet is hit with death at a time you can use another's action to do a restore, particularly since death doesn't actually take a soul puppet's hp to zero.
Second, find a soul puppet with a resurrect or healing ability (I had a nurse undine that rocked for this).
Third, Try death resistant gear, this often works, though manifestly just restores the chances of death, still, death attacks rarely hurt much and have only chances of working anyway, so restoring gear is good.
Fourth, use status effects that stop the enemy from acting. Really, sleep or petrify can often be your friend here, indeed I've got through several very tough boss fights by spamming sleep and poking away, silence is also good too.
Hth.
Sorry I can't recall which enemy that was precisely and I've not played puppet nightmares for a while, still it always was a very awesome game and I'm glad your having fun with it.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)