If it's any consolation, she only shot Annabeth because she was struggling to make it through the snow. That weakness would get her killed, so Lucy shot her in the guts to prove that point. 

There was also ten recruits at first. When Lucy told them what their traini g would be, two of them tried to protest the insanity of it. Being the charismatic woman she is, Lucy killed them, but at least only after they kept up their "wasteland badass" attitude. She quickly proved to the other survivors that the wasteland has nothing compared to her. The others died one by one during the training, though one did try to get away when they were told to cross a river. Testing out her new array of VATs skills she killed him.

At some point I do expect someone to try to at least ask her about the insanity of her tests. She'll go on a tanget, but she won't actually tell you the full motivation behind it, just the ideal she's striving for.