Aha! Thanks to the wonderous magic that is this page on GameFAQs, I found out what I was supposed to do and worked my way through the missions some more. The path between them branches a bit, it seems, but you still need to do them all to progress – I’ve completed Grassland 2-1, but I can’t move on to 2-2 until I finish 1-7.
Which isn’t going to happen any time soon, since I have to destroy all the walls in 60 seconds. I managed about 50% of them in that time, after about 10 attempts. I just can’t get enough hits in quick enough, and some bits of wall I can’t even reach to hit. Pff.