Some of the improvements come from lag reduction. At the start, around frame 73700 and on, you get three lag frames fairly quickly. All of these can be avoided by jumping at the right times.
Then there's the climbing, which is technically faster to do by simply jumping straight up, though the camera won't catch up as quickly, which is a problem...
Turning around is another thing that could be improved. As if you jump left to clip into a wall, with the intension of going right afterwards, just holding Left to frame 5 and press Right on frame 6 is rarely the fastest. But instead you might want to have a frame or two of blank input first, or maybe left, blank, left, blank, right, right etc. or left, right, right, right, blankt, right etc. etc. It's tricky and annoying :/.
Here's a short and unoptimised sample of the climb:
http://tasvideos.org/userfiles/info/35325766206140238
I reduced the lag mentioned in the beginning, though didn't bother with the ones at the climb itself, which could probably be reduced as well. I also took a different route to avoid bumping, though it takes longer to drop down before you can start the climb, just an idea.
I thank you for this and don't try to optimise it too much, I suppose, as fully optimising this is death itself :/. I'll be happy with anything really and obviously giving you full credits for it with assigned author, if you wish.