As the topic title says. You need a move from the other level in each level, so you cannot finish the either level without hitting up the other. So, I'm curious as to what the fastest way to handle this is. Run into one, grab the move and leave? Do everything possible in one, clear the other, come back for what was missed?
Here's what I've read and tried, it's actually very interesting (some of the prep stuff might be out of order):
Open Gobi's Valley, go to Freezeezy Peak, learn the Beak Bomb, then leave immediately. Then do Gobi's Valley, but before you go back to Freezeezy Peak, open Mad Monster Mansion then complete that level. After that, beat Freezeezy Peak, and here's where it gets interesting:
For the Witch Switch Jiggies, get the Freezeezy one first, then using the Flight Pad in the Freezeezy wall, Beak Bomb the witch's eye for the MMM WS Jiggy.
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Depending on how abstract you get and how closely you're following recent developments in B-K speedrunning, it MAY not be necessary to double back at all. However, for people who aren't going to do crazy, frame-perfect tricks and the like, I recommend downloading the video linked near the top of the page here:
I'm pretty sure DonkeyKongSong has the gist of it right, but it's been a while since I watched the video, so you should check it out if you have a chance.
Personally I've always completed a level before moving onto the next then came back, but I was never trying super hard for a speed run.
That being said, what DKS said is probably the fastest. That way you aren't wasting time going back to the level then running halfway across it just to go get the jiggy you missed. Learning the Beak Bomb is pretty close to the entrance to FP so you won't waste much time learning that and getting out.
You can always experiment, of course. But this just seems the most likely.
Black Mage: Dammit fighter, White Mage doesn't like me because you're a rotten friend. Fighter: I'm horrible!