If you are having trouble making certain Mushroom types appear, do this: Go to the Final Rest area in the End of the World, and save your game. Do a soft reset (L1, R1, L2, R2, Start, Select), and reload your game. When you exit back out to where you fought the Behemoth, there is a very high chance that you will see one of the three types of Mushrooms. After you have what you want from the mushrooms, head back to the Save Point, save your game, soft reset, and repeat the process all over again! This technique is particularly useful for finding Rare Truffles, and the large, circular-ish room is ideal for batting them around.
If you're looking for White Mushrooms, you're best off searching elsewhere, where they will request more specific spells. Things can get quite frustrating since they have all 7 spells to pick from at the End of the World.
As well as this trick works, I barely ever find Black Fungi here. Instead, I like to hunt them in Hollow Bastion. Ride the platform down into the Dungeon area, and fight whatever appears (hopefully the Black Fungus), and then head back up, and take the elevator to your left up again. When you head back down to the Dungeon, the enemies should have respawned. I find that the Black Fungus enemies appear a lot here.