You can just ride the "This must be the way down" platform straight down; it destroys the spikes beneath it, making it safe even if you jump.
You can flip-hang safely into spikes one tile lower than you, which lets you get into the room from the left by entering the spike pit.
You can also safely fall into spikes if you use a cape, so killing the vampire lets you enter that spike floor another way.
And, for the really hardcore, it looks like it might be possible to get both red frogs closer to the spike floor (by having them each hop onto a block and then the tree), then killing them one at a time and, with perfect timing, tossing their corpses at the (not-so) deadly shaft, destroying the wall on either side of it and creating a gap that'll let you into the room.
All of that's supposed to happen. Which is why is why it's only medium.