It's an interesting one. Not sure if his kind of shield would be effective or not, though writers often give the benefit of the doubt to shields with those things. On the other hand as an Eternal (and one of the most powerful) she has complete control over her own molecules so I'm not sure what he could do to her either. She has even reconstituted herself after being disintegrated. And anything he throws at her gets transmuted.
I wonder if she could try sneaky things like subtly altering the air with chemicals or removing the oxygen in a wide area around him - he has to let air into his shield eventually while she doesn't need to breath.
I'd give Sersi the slight majority but It could just come down to who makes the first mistake.
I dont think they allow air in and out, he just breathes his own little atmosphere in there, prolly recycles it too. there is also the fact that their functioning mechanism is not real physics, but plot necesity. for instance: he is visible inside them and can see people outside, but laser beams have a fat chance of getting through. same goes for sonic attacks, even thoguh he carries converstions throguh those things. so even if he breathes normally, I doubt a harmfull gas would make its way in there.
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and i tried some sound attack or something.
and i agree with 753--it doesn't really seem that air would get through logically--and by logically i mean comicbook logic. but by that SAME illogical-ness ( ) it COULD mean some poison air could get through. i wonder if it has ever been brought up? where's bats, he might know? he's usually watching, hovering silently like a ninja, waiting to strike.....