My vision of this was to add dimension to the face, add depth between the bird and background and control how the light was perceived.
Main features of processing were:
1.mask to lighten face and shoulder. Used curves adjustment layer with the face and shoulder selected. A radial-zoom blur was used to feather out the transition. Painted some areas with greys depending on how much I wanted to show/hide.
2.gradient layer to warm it up and give it a sense of light direction. Opaque orange going from dark on left to light on right. Erased some on the right to get a truer green in the top corner.
Also sharpened, did some selective satturation on eyes and beak.