6 years ago, I discovered a new type of ghost glitch hat allows to skip most of the Level 5:
http://tasvideos.org/userfiles/info/35187178884407627
It only works in lava, but have to jump enough to touch the lava raised. If it works properly, it will appear that fell into the lava, but actually jumped to the other side. But this bug, is supposed to be dead and can not press switches or move while using the sword (Unlike that ghost glitch of Stage 9, which is possible to activate without fake death, allowing to push switches and uses a sword).
In other words, this new bug is caused due of bad collision detection on rising lava.
This glitch saves tons of time! (EDIT: 2479 frames saved on Bizhawk).
Another thing: During my tries to encounter other locations to activate this new ghost glitch without lava (or fake death), accidentaly I discovered 2 big new shortcuts! One of Stage 6, and other of Stage 7.
I discovered these shortcuts two hours ago.
Stage 6:
http://tasvideos.org/userfiles/info/35234092789957410
EDIT: I tested a different (and faster) stategy than this file, and I saved 1117 frames on Bizhawk.
Stage 7:
http://tasvideos.org/userfiles/info/35234125916635235
EDIT: Saved 1104 frames.
This glitch is only possible on SNES port, if you grab in a wrong position next to a wall. It works in a very some platforms.
With these new improvements (4700 frames totally), it's now possible to a new TAS of this game beats on almost 10 minutes! I'll assume this new TAS!
EDIT 2 (28/11): Stages 1-6 finished! 4014 frames ahead of Alyosha's published TAS.
EDIT 3 (29/11): Here's a WIP:
http://tasvideos.org/userfiles/info/35308479530060816
Levels 1-9 finished! 5304 frames ahead of Alyosha's published TAS.