That hill level (3-3 is it?) is a bitch if you die right after getting the fairy on the downhil. It's basically a walk away moment because next time you get that same egg for the fairy, you get an axe, which is no good for walking through 8 rocks in a row, and they are too tightly spaced to try pixel perfect jumps in between.
Because you get stuck tripping over the rocks repeatedly, your vitality will just drain to nothing, and then repeat again and again.
Just one case of the 'I got 99 lives and I'll be losing every last one'