Also I wonder if you should switch the second and third levels: I find the second one to be the hardest. There's nowhere safe to stand; the blue enemies jump high enough to miss your sword when jumping onto the starting platform, and you often have to go through the danger zone at the edges where enemies can wrap and the timing is hardest to predict. You have to judge how fast the enemies are moving relative to the saw blades and whether to kill them and then jump the saw blade or to jump the saw blade, turn around and then kill them. And you have to be very diligent about keeping the enemy population down or you get into difficult situations.
Whereas on the third level you can safely stand by the door and kill all comers. If you stand on the edge of that platform you can reach the blue guys before they make their first jump. From the second platforms on the edges you can get *almost* everybody: you can hit the blue guys as they jump in or as they jump up to where you're standing, you can get the blue guys on the long middle platform; the only real danger is the floating heads coming in from the edge. And you can make it to the top edge platform in a single jump, so the only time you even have to go on the one with the saw blade platform is if a lantern drops there. The only thing the saw blades really do is make it dangerous to jump when you're on the door platform, but you have no reason to ever jump from there, except out to the edge platforms where you're mostly out of the way of the saw blades anyway. And even if you let some guys go by, it's no big deal; they're mostly out of your way and you can just kill everyone coming in and wait for a good opportunity to clip the missed ones from one of the edge platforms.
Can you tell I've spent *way* too much time playing this? :)