I drew some lines to approximate the normals of the surfaces. You have inconsistent light sources that differ from his cheek, beak, and around his eyes.
Looking at the beak, the pointy end of his beak receives the darkest shade. If you look at the surrounding normals of that area, you'll see that they're quite close so it shouldn't be so dark.
Similar issues occur around his eyes and the back and top of his head (especially that large dark brown band).
Here's my attempt at Kent:
I didn't prefer your contours, so I drew my own. Yours are fine, but I prefer to have constant slices. The vertical lines show a X slices (varying YZ) and the horizontal lines show Y slices (varying XZ). Due to my contours, KentC appears to be viewed from above, front, and a bit to the left relative to his face. I also changed the shape of his beak by pinching the area below his nostril.
The light is aimed down and to the right relative to his head. So I shaded the faces whose normal pointed away enough from the light, which include faces that point downward and to the right. Note, I shaded Kent's entire jaw since it's occluded, it's normals are aimed downward, and it's simpler to one have one large shadow.
I didn't see a need to have multiple shades since I made the lit surface threshold pretty large.