This was such a fun concept! I really liked the idea of having to jump between dimensions to make it to the end. I agree that the controls could use a bit of tweaking and it'd help to have some kind of background music to get the player more pumped up while playing.
Also, not sure if this was a weird bug but for some reason my character kept dying back to back until I ran out of lives. To be more specific, something killed me near the flag and then when I respawned I immediately died again (and again) until it was game over.
Overall, this was well done! Great job!