Play as Jigglypuff. As soon as you possibly can, dash to the edge and jump off. After one jump, let yourself fall under the level, then jump back up around the underneath of the level and grab a hold of the opposite side you just jumped off. fall from the ledge, jump towards the edge of the screen once, then fall back under the level, jump up from under it, and grab on to the opposite side again. Repeat.
The AI seems to be particularily bad at judging how far it can jump off before there is no chance of getting back, it seems, I've reached about 10 or so with this on my fourth-fifth attempt because they keep on self destructing. The only problem is getting the graan alloys down because they have the 6-jump ability, so you need to smash them down once they're below you.