Ignoring
@B_023 's stalker cliff notes often misrepresenting what we actually write...
Stuff like character ages isn't "canon" so just trust your own impressions. There was a similar debacle with the MC's age based on his appearance in certain scenes vs. a throwaway line in a Yvonne grapple. Ultimately Bo simply didn't put much thought into it, so putting exponentially more thought into debating or analyzing it is a questionable use of time, but have at it if you please.
Anyway, it seems obvious and well-established within the text that the MC isn't necessarily "beating" the girls so much as proving himself inconvenient enough to tame that they just let him proceed. Cobra is a bit unique in that he leaves with her blessing rather than her frustration, but if you legitimately thought she'd been going all out when she already took down Gerald and his entire crew at once... I'm not sure what to tell you.
The exact nature of her "conveniently" shifting power-level is explained in her EX unlock text, with her EX-levels in general being probably the most lore-friendly and most explicable as actual power that she justifiably has access to based on her backstory (ie. perhaps contrived, but certainly not ex machina).
Compare with Lily who relies on a magic artifact; Khulan and Eliza who appear to be channeling some sort of ambiguous barbarian rage / holy power respectively; Yvonne who is just plain angry; and Scarlett who I'd probably rationalize as not even fighting better but simply psyching the MC out with her increasingly dominant aura as she gets more serious... and it seems weird to single out Cobra as being the hand-wavey one.
If that aspect of the plot disastisfies you, that's fine, but it is fully manifest in the game text and not a dev addendum.