Consider she got an average (if a bit perverted) dude to
survive three vampire hunters, exorcise a cat youkai with energy draining abilities, then exorcise minor kami, break a wishing curse feedback (
surviving a grievouly battle in the proccess), another double curse, and then a professional exorcist.
Most of the time she is the silent mentor type, or keeps out of the picture, but if her quarry is threatened,
she can teleport out of his shadow and dish the beatdown. Keep in mind, the cat-eared girl defeated a experienced exorcist previously, and the loli form of the vampire is because she is very low on power.
If Shinji got through half of what Araragi survived, the disturbed plots of Nerv won't be that much of a trauma to him, and I'm pretty sure he will be able to pilot an Eva through even more bloody battles too.
For an philosophical series, Kizu/Neko/Bake/Nise-Monogatari has pretty bloody fights.