After Thaviks disappear and goes invisible after taking damage, it is possible to see him climbing the walls on the arena. If you shoot him, he will fall off and instantly die, ending the strike
Video proof: https://youtu.be/eCRjzlDBuCY
I assume this is a cheese.
[spoiler]Video not mine[/spoiler]
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I can't confirm if you can kill him or not but before failing miserably at the NF, we got him to half health as he was crawling along the wall after the first teleport. I was using nightstalker and hit him with a super/smoke nade combo and I was Also using the exotic hunter helmet that tracks enemies. I saw him run along the top as he was marked by the X. Was way too fast to put any real damage on him though. You'd have to be on point to get him if it were possible