Opening the map and talking to the spirit (d-pad left/right and A) on the same frame makes it possible to close the map immediately instead of having to advance through the spirit's text boxes on top of the map.
This does not work on Wii due to the priorities of the map and interaction being flipped.
After listening to Coro's spirit, charge up and target both bugs, then turn off senses slightly before or at the same time as releasing the charge. The bugs should die before they disappear, which will skip Coro's text that's normally there.
With good rolls and movement, it is possible to make it past the purple mist area with just two lantern swings.
Rolling closely around the broken bridge is key to making it and not voiding right at the edge of the fog.
Voiding in the purple mist to reload the area after the cutscene makes it possible to attack the bugs before they dig underground. This is slightly faster than waiting to dig them up.
There are several instances in Faron Twilight of single frames between cutscenes and/or text boxes where inputs can save time: