The first episode was the first occurrence of the event, so she was actually killed then (presumably by her father). Later on, he went back in time to try and stop it and changed it so he accidentally killed Kurisu himself, then changed it again so he tazed her and then covered her in his own blood to make her only appear dead.
@Zexion - Yeah, ShidoZ's right. It was his text to Daru that actually sparked the leap onto the alpha world line, so whether Kurisu really died or not didn't matter. He just had to ensure that his past self thought he saw her dead in a puddle of blood, that way both his memories and the faint ones Kurisu and the others got would remain intact.