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It's possible. I had to complete it that way myself some days ago, because the rolling while running-button didn't work on my old keyboard. To complete this, you can't just run like usually even if you were super fast, you must use some special tactics.
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Post a video to prove it.

Also, I have some ideas for challenges:
Slap as many glukkons as you can.
Kill as much as possible.
Kill as little as possible.
Use run-jump-hoist as little as possible.
Use sneaking as little as possible.
In the 4-minute boiler run at the end wait for 2 minutes after turning the wheel that activates the timer, and try to beat it in less than 2 minutes.