It was a solid experience. I liked returning back to the beginning. Managed to collect 14/15 souls.
The music was alright and the shooting sound felt good. The dying/reviving effect could have a bit more juice in it.
Visually it ain't the most striking, and the character seemed a bit out of place with the style. I liked the BOOM effect on the shotgun fire though!
I didn't get at first that I could use the shotgun as a double jump, but it didn't take long to understand. The ghost/reviving mechanic is neat. Although it can lead to some infuriating situations when you miss a jump and fall on a pillar... and you end up right at the bottom of the map. The jumping didn't feel very good sometimes: some collision glitches when you jumped near a wall or some platforms.
The enemies could use some more effect when dying, sometimes I'd second guess myself if I actually hit them, until I saw them falling through the stage. Perhaps some sprite flickering or color changing?
One thing I noticed was that the shotgun effect moves as you move the shotgun. Not sure if you used a particle system in Unity for the smoke, but if you did, changing the simulation to happen in World Space could fix this, once the particles are at their position, moving the character wouldn't move them around. Sorry if that seemed pedantic!
Overall it is a quirky platformer, enjoyed the ghost mechanic. Could be used to add lots of depth if you plan on evolving the game.