I'd say she'd get some nasty cuts in the process (ones she wouldn't mind much, mind you), but Menagerie would drug up, claw up, or acid-burn Warren into submission a large majority of the time.
It has been a long time since I read JLE but when was Menagerie ever shown to have regeneration or a healing factor? The first one is still hospitalized because of a stroke and I don't remember her sister ever healing either. Seems like a stretch to think she could beat Archangel to me, Warren incapacitates her with nerve toxin feathers.
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The symbionts can't fix the brain, hence the stroke problem, but they've done eyes, chest wounds, etc..
Heck, when Superman took out the first one in the famous Elite fight, both of her legs and one arm looked like they were either no longer attached or attached only by bugs.
And like the others mentioned, they do drugs a lot.
Can you post a line of narration where it states that Menagerie can heal, and that her healing factor doesn't work on the brain? Because I don't think it has ever been said or suggest that she can regenerate. There was that a single scene where she was shot with some cross bow bolts while Sister Superior was pretending to be Deathstroke, but they "weren't supposed to hurt," and it was all part of an elaborate ruse that among other things involved Cold cast getting his head cut off. Nothing I would hing an argument on there, especially given the context of the incident.
That scene you are talking about was just the bug symbiot being "blown" off her body, her legs and arms weren't blown off. You can see her perfectly fine in the next panel, just sans symbiot.
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Some of the arrows were sticking out of her back, all the way through.
And she pulled them out and we saw them- they were still full-length bolts, and one was in her eyes. The physical dimensions after removal said it had to be through her eye.
It probably wasn't supposed to hurt because of something put on the bolts to make it less painful or something, but... they were physical objects going through her, clearly shown on page.
Her limbs were in a position where they could not possibly be without being detached, but bugs did connect the parts.
In other words what happened is exactly fitting with the bugs pulling her back together after a major blow.
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Other injuries include Wonder Woman cutting open her stomach in the JLA vs Elite fight, then you have the Blood Brother with the burning hand burn her neck to the extent the blood coming out melts his hand and her neck being fine after with no sign of pain.
She gets injured often and is always fine with it unless it's a fairly catastrophic blow.
That is true for every character, having her stomach scratched by WW whip and continuing to fight is hardly evidence of a healing factor.
The body could easily contort in that manor, arched back on a downward slop with the legs bent. You can even see where the breasts and shoulder were supposed to be if the colourist had done his job properly.
I'm pretty sure she was shot in the back and the front considering the bolts were only about four inches long.
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It was just a slash to the midsection, incidental damage like that disappears all the time over the course of an issue. I've seen Wolverine regrow a suit in the middle of a fight. If she had been eviscerated then it would be notable, but as it stands it's not much of anything really.
Two of bolts in her back look like they might be arrow heads, but none of them, front or back, have fletched ends in that panel. The fletched ends are visible in the panel where she is removing the darts and the are all on the front and darts are only a few inches long.
The hypothetical shoulder is the blank spot to the right of the ear and if you drew a slightly curved line from the elbow you would find the spot where the waist would be. As an illustrator myself I'm well aware that the foreshortening and perspective aren't perfect (the art in the issue is pretty awful on that front, it looks like scrap book of people from different photos and different angles pasted together) but if anything the spine would be too short.
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