The problem is that the animation frames are never the same size, have wobbling origins, and dancing collision polygons.
The character 'falls' during playing an animation, even when it is standing on a platform. The 'is stopped' never triggers. Either vector X or vector Y is always shaking. As a result almost none of the build in platform triggers is reliable.
Solution: or fix the animations,
or use a basic sprite with the platform behavior and pin the animations (as the eye-candy) on it.
I did choose for the last one. Once the animations are 'messed up', it is hard to fix them.
https://www.dropbox.com/s/zlgnz0l6f3w0t ... .capx?dl=0
Besides that, plz consider using tilemaps, instead of big sprites.