This is the short guide for the glitch skipping all levels of Zipsa besides Spider Web (which kinda is a wrong warp, ngl): TL;DR: Have a cat bird save that hasn't entered Zipsa yet, after finishing both Marda and Grasi, enter Winda over the time trials menu (finish it) and then enter Zipsa over the world menu. The cutscene plays and you land in Spider Web.

Why this works (probably): The Zipsa entry cutscene seems to only set your world ID (iirc it's just an integer from 1 to 4, determining what world the level you are sent to is in) to 4 and doesn't mess with your level ID (which is an integer from 1 to 15, actually determining the level). This is why when you start with a fresh save, only play through Hello World and leave from The Pit, the cutscene sends you to Telejump [this is what happened to quite a lot of people]. You could use this to get to your favorite Zipsa level without playing any other Zipsa levels on such a save by playing Marda until the level number you're interested in in Zipsa, leaving the level and triggering the cutscene, which will send you to the level of your choice. For speedruns, another fact about the level and world IDs is important: The Winda end cutscene sets your level ID to 1 (because it seems to fundamentally just be a copy of the Marda->Grasi/Grasi->Winda cutscene, just without setting your world ID one higher, because the cutscene was made before Zipsa). However, under normal conditions we have to watch the cutscene, because it plays when normally finishing Big Bear, which is necessary for the speedrun. To avoid this, you can leave Floater after being sent there from Mad Totems and enter time trial mode for Winda, which will stop the cutscene from playing and thus preserve your level ID of 15 and not start the Zipsa cutscene automatically.

(By the way, this does not work with the cutscene replay, because that one just sends you back to the level select. If it was supposed to send you to The Room instead, it would work.)

Here's a video for it: