I'm really happy to see that someone has decided to improve this TAS, as I've been wanting one for ages, without having the determination to make it myself.
There are a bunch of places where you can use, what I call cancel climbing, to get past screens faster. Cancel climbing is something you can do as you wall jump. If you use a ninpo at the correct time, you cancel your outwards momentum, and can get back to the wall, gaining height, effectively climbing the wall. It's tough to do in a RTA, but worth doing a couple of spots.
The main problem with it, is that it requires ninpo to do, but since you can get infinite ninpo fairly quickly by increasing your ninpo to 999, it's not really an issue.
I also stumbled across this once or twice: https://www.twitch.tv/videos/49391400
Not really sure what happens there, but what I think happens, is that you fall through the floor, and start screenwrapping vertically really fast. You can still get through the level, but you're invisible and enemies don't hurt you. I've theorized that it's possible to do on any screen without a pitfall, but that might not be accurate.
Don't hesitate to ask if you have any questions about this game, as I've been playing it for a few years now, and know a lot about it. I can't wait to see the new and improved TAS. I really think it can go sub 14.