I have never watched Sword Art Online so I don't know how to give more insight to it other than what I could notice from this story. Okay, so from what I gathered, I don't think you have much issues with the tenses, although there was a little bit of fixing that could be done like in the first bit where Kirito asked the executioner something and there was a lack of punctuation in the beginning of the conversation.

The other was the part where Asuna was angry after all that happened, and something along the lines like 'but the mind is much more logical than humans liked to think' - perhaps you could change it into 'was'. 

Other than that, I think that your writing's good so keep it up!