21 frames improved from #5401: fsvgm777, ruadath & TaoTao's NES The Quest of Ki "warps" in 02:27.51. You can decrease stun time by pressing A.
You can take a shortcut with high-jump. But logs do not work as expected, so I might not achieve so large improvement as I thought.
I succeeded to manipulate the purple enemy. It seems to be related to the timing you kill the first dog. But I still do not know the mechanism behind it.