Yes, she hesitated, but she did try to kill it in the end.

That's why Tatsuya told her she's not cut for this job. She is not a cold-blooded killer. But she is capable of killing people, and has done it before.

So when she tried to kill Tatsuya at the beginning of the series, and now when she straight up blew his arm, she clearly defined herself as hostile.

Yes, she won't kill someone without a thought, like Tatsuya would, but she is there because she's capable of killing, just like the jocks who assaulted Tatsuya at the restaurant.

That's why I think it's not ok to brush this off just because Tatsuya can regenerate his body at will. Because if he wasn't able to (which is what Lina thought) then he would be maimed for life, or dead.