Very clever! It felt a like a nod to Braid but with its own mechanics. I really like the idea, though there are some parts of it that can get a bit frustrating. Part of it is the precision required combined with the one-hit death part. Maybe if there was like a paradox meter that you fill up as you make mistakes to make it a bit more forgiving? Maybe two or three chances?
The platforming felt very "heavy", for lack of a better term. Up and down goes very fast, which adds to the difficulty in precision (perhaps on purpose?). I also would have liked some more forgiving hitboxes for the coin collections. Sometimes it felt like I was jumping past a coin but still collected it.
I loved the detail of the princess always moving backwards; that was nice. And having the coin counter and HP in reverse was very cool, though it was unclear whether that needed to be met by the end? (It didn't seem like it did.)