Well I didn't expect to save 7s just by optimizing my movement and combat a bit. The changes I made was to just skip the Blade Mode (except for one Dwarf Gecko) and just use the 3 piece combo of Light Attacks instead. I did add some Vault Jump Cancels, which maybe adding more could save additional time as well. I also used a Lightning Strike Cancel at 0:23, although I could probably do it way earlier than I did in this run.
The biggest hurdle with this mission is the mine cycle at 0:32. I think if you're fast enough to catch the cycle just as they go down (prior to jumping and destroying the Dwarf Gecko), you should be able to also have time left to also get out without having to wait. I played it safe (I don't think I was on fast enough pace anyway), but there's a potential of 1-2 seconds at least to save in the future (maybe). I think also maybe another Lightning Strike Cancel could be added at 0:38 to save more time, so that's worth checking for future runs.
I think this level can easily be pushed under 1min, and probably way lower. The movement isn't even good, as I mostly just do normal Ninja Running or jumps (no Bunnyhopping currently). But that's for another time!