Been a while since I played this, but you get keys by beating the bosses iirc. Bosses respawn after you clear a few other stages a couple times
I replayed at least one of the bosses, the bit fungus/toadstool thing with a humanoid figure that pops out of the center. No key yet. I'll try some more.
A more critical problem I hope you can help with:
I can't clear the "Beyond this hill" stage. When I reach the place shown in the screenshot, I go to the right and down to a pond. After clearing the monsters at the pond, I go up and to the left and back to the screenshot, but I can't jump her up to this ledge from this spot in the screenshot or from another ledge to the right:
I assume that when I get up there, I can continue to the exit. Since I can't do that, I give up and go back to the entrance but find that the stage isn't cleared.
I went back a couple of times to try some more, but still no success at that ledge.
Forget it, after hours of attempts I finally made the jump. LOL
And I found a couple of those keys, as well.