LIMBO style 2D character controller?

Hi all,

I am wondering how I would begin to approach creating a LIMBO game styled 2D character controller? You can see it here...

I have a fully rigged character exported from Spine with IK, and have been messing around with it, but with not much luck so far.

Has anyone attempted this and could give me some pointers? Perhaps there's a demo project out there that I could look at? How the heck did they do this?

Any input is greatly appreciated.