In EoE, Asuka soloed ALL the MP EVAs until they got in a surprise attack with a copy-lance going through her AT Field like it wasn't even there and trashing her arm. Then a follow up attack through the eye, and then her battery ran dry and she was helpless. When it looked like Unit-02 was about to go Berserk the MP EVAs pinned it to the ground by turning it into a giant pin cushion with the lances, stopping the nascent Berserk in its proverbial tracks.
The implication is still there that for all the external damage she did, Asuka's last stand didn't do anything to stop the MP-EVAs themselves, or even so much as make them do anything more than stop messing around. They were purpose built to offer up Unit-02 as a sacrifice and use Unit-01 as a vehicle of apotheosis. So unless SEELE is run by incompetents, the controlling element of the MP-EVAs should have been made to be better fighters in every possible way: agility, strength, numbers, weapons, and tactics. They also seemed to lack the limitations of human pilots, namely any kind of pain response or internal organs.
Yeah, she mopped to floor with them for a bit, then the got back up and skewered her, with little regard for the damage they took.