This room uses a weird quirk, though it's one that makes sense given some other weird quirks.
Here are some hints on what that quirk is.
General hint:
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×The order in which things happen within a turn is relevant.
More specific relevant mechanic:
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×When you stab tarstuff, it is not actually destroyed in the moment when you stab it. Rather, what happens is that the game notes that a particular tile is stabbed, and then at a point after monster movement, all those stabs are processed at once. This is what makes multi-stabbing work.
Less obviously relevant:
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×An entity with a sword will only stab either on its own turn in the move order, or when it's pushed. So if a monster is pushed under the sword of something that's already moved on a given turn, the monster survives until the next turn.
How it fits together (solution spoiler):
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×Stab the tar and have the stalwart push the mother under your sword on the same turn.
Because tar processing is a separate step, the tar blob is stabbed. But the mother isn't stabbed because the stalwart's move happens after Beethro's, so at the end of the turn you have a living mother under Beethro's sword and no tar.
Fortunately you can do this pretty early in the room, before the first spawn.
