How does Kirito come back to life when he's fighting Heathcliff? I was rewatching Sword Art Online and I notice that Heathcliff KILLS him and yet, he is able to come back and finish off Heathcliff, how is this so?
Logically, there is a delay in between the death flag being detected and the NerveGear frying the brain, which is explain by how a Revival Item (Divine Stone of Returning Soul) can be used within 10 seconds of a player's death.

However, as for how Kirito, whose HP was 0 but was still able to affect Heathcliff, was explained by Kayaba Akihiko when he congratulated Kirito for doing something that went beyond the system by using the power of the human will. This concept is reasserted when Kayaba appears before Kirito in ALO and reminds Kirito about how he acknowledged this.

It's more of an anomaly rather than any sort of plot hole. In essence, Kirito shouldn't have been able to do anything when his HP reached 0, but he was still determined to end the game because Asuna believed he would end the game for her sake. That determination allowed him to transcend SAO's rules.