This is internal monologue of a character about another. Also this is from a manga so there is no punctuation.
この子は時々まるで『自分』を省みないような
それこそ普通はためらうような… 命を投げ出す行為を平気でしてまう
This is my current interpretation:
This girl sometimes seems like she doesn’t care about “herself” at all.
That for sure is how she normally is, seemingly hesitant… about actions that completely and remorselessly sacrifice lives.
The second bit is a bit dubious. It is characteristic of the character being described, since she never hives up on people, it still feels weird in context.
On the grammatical/language side I'm assuming それこそ普通 is basically saying that she is like that normally こそ is intensifying this but Im' not 100% sure since I haven't encountered それこそ before.
Also I'm not sure what's being described as ためらうような hesitating like? How it's normally?
And of course what's your read on this sentence?