I estimate you can get down to 3-4 min at least with just learning the levels with minimal execution skill, below that is where movement tech comes really into play
UPDATE: i got 7 minutes, dont know how someone got 58s
woooooooooooooo \o/
if you want spoilers, there is a speedrun by me (now super beaten 1:15)
https://www.youtube.com/watch?v=cbyMrR4TooM