The drop after the hatch with switch gives the player no way to avoid the enemies at the bottom. Similarly, the start of the second stage gives no way to know where the platforms going down are. There's nothing to indicate that the player is allowed to jump to swim out of the water nor that the water will slowly drain the player's health. Later in the stage, the safe paths get too confusing, and it's not clear if it's possible to win without losing half the maximum health.
The jumping doesn't feel good. Try to avoid jumping mechanics that don't resemble the overall form of real life physics. In this case, I'd recommend an initial jump boost when the player presses the button, followed by one of two different rates of slowing down depending on if the player is still holding the button, then on the way down a single rate for speeding up to the maximum fall speed to represent gravity. That way the over path is similar to a parabola (a specific type of U-shape) but still giving the player control over how high they jump.
Lastly, the image for hearts being gone isn't very clear. If you use that image/style again, I'd recommend either changing the color of the heart itself or putting a lot more scribbling on it.