I just saw it... wow, I can't believe it
General playstyle is LoN FoK: Hold down Strafe, tap Evasive Fire (works well if you hold down force attack while strafing), use Preparation / Smoke Screen to survive and move. Make pulls and blow them up on lightning CoE with FoK. The setup is EXTREMELY unoptimized (p140...), you need Obsidian procs to reset Vengeance in time, and you will run out of hatred if you don't weave in a few generators without channeling Strafe, so try to do that when things are relatively safe.
Pro tip: Make use of the little area damage this build has, only use FoK when you have an actual pull (preferably around elites). If you watch the VoD, you can see I did most of my cycles in 16sec instead of 32sec because the damage was pretty good on tier 45. Good thing about challenge rift is that pylons will already be there, so the run can be optimized to play around that since you don't actually have to kill anything to spawn them (channeling early can be used to skip the floor, conduit later can be used more effectively).
Edit:
6min clear. Got quite lucky on almost all crits, just had a bad noncrit on RG (so lost 32sec there). Compared to the original run, I skipped more in first floor and went into floor 5, which is pretty good.
Full breakdown:
Floor 1: Enter at cold CoE, skip blue fallen, rush to and kill yellow zombie, click channeling, rush to and kill blue crawlers.
Floor 2: Kill yellow trapper, kill blue cultists, click shield.
Floor 3: Trash pull, trash pull, kill yellow zombie, trash pull.
Floor 4: Rush to and kill yellow thrall, kill blue maggot broods, click conduit (finish off old elites if they are low), rush to and kill yellow cultist, rush to and kill yellow crawler.
Floor 5: Rush to and kill blue berserkers (important: they have shielding, you need to time it). Kill yellow trapper, kill yellow ghoul, spawn boss.
Boss: Keep up Vengeance and dodge, he can kill you. If you are lucky, you need two crits (1 with ambush, one without) and he might die or live with ~5% hp or so. With single out you have 71.5% chance to crit, in total 51.1% chance to crit twice in a row. So in the end it will be a coin flip if you have less than 1min left.
My original run was also relatively lucky in terms of crits and I actually took an okay route when I cleared it for The Thrill, which makes it hard to really optimize or even just clear the rift for many people.
Edit 2: Fun fact, in my original run I went from P138 to P143 without assigning any points, in the challenge rift I'm 143 with all points spent!