@Nixolas_Zinn I think you dont understand anything, because we dont exactly know how much days passed, how much he investigated AND he did something that only attacks undead. Every living person would have been fine, what he even explains in this chapter. (Which implicates how you read such things .... not good at least.)
He got her offguard, when she believed she won and tried to kill him. (Pretty legit self defense there.)
Then she spoke about another person, which could be a mastermind behind her (also because she is an undead or rather intelligent undead) and who would be the true danger.
So where is there a problem again?