As stated before, the "dude" armed with semi-modern small arms managed to take down Lady D in a mutated form that was only triggered when she was stabbed with some super special dagger that was apparently laden with toxins or whatever. And even then, the "dude" had to shoot at Lady D in the humanoid form that was on the back of her monstrous form because the rest of her body was nigh immune to damage, like she is nigh immune to damage in her basic Humanoid form. If this scenario was a scripted boss battle, then surely Horrigan could pull off a similar feat, but this Versus isn't a scripted Boss Battle. She doesn't need to oblige.
If we're talking about shrugging off, Frank Horrigan is actually harmed by whatever an "industrial plasma caster" is as in he incurs hit point damage. Meanwhile Lady D can literally shrug off all manners of weaponry. This could be argued as due to gameplay mechanics as she's shrugging off M79 Grenades to the face and walking over anti-tank mines with nary a concern in the world. It is notable to state that her staggers tend to consist of her brushing off her dress or straightening her big hat. Compare this to say, Nemesis or Mr. X from the earlier Resident Evil remakes who actually visibly stagger when struck by things like overwhelming amounts of gunfire or explosives which would seem to imply Lady D is more resilient then those Tyrants would be, gameplay mechanics aside.
You're debating using game mechanics as gospel, that's a little dishonest, come on.
She's a nu-MrX type enemy who cannot die until scripted in their boss fight, by that logic can you nuke her and she'll walk it off? What about a tank?
Seeing as every other boss in the game is vulnerable to small arms fire (well, maybe not robot dude...) she is logically no different.
The dagger certainly weakened her, but I'm pretty sure that some of the most powerful fallout weapons ever seen should be able to at least match that level of damage lmao.
Horrigan ignores gunfire in one of his cutscenes, canonically he's tougher than the bossfight.