This tutorial is an editable to show how the layers work. Feel free to add in your own layers to try your own steps.
I started with the paint brush to get a general sketch, then added a dark, de-saturated under painting underneath it using the ink pen.
Sketch was set to overlay and from there abused the color picker and blocked in colors while adding in new colors.
Next step is just focusing on the shapes of the clumps of fur and defining them. With each step there is always some tiny amount of the layer underneath still showing to allow the look of an undercoat.
For the last details darker areas are color picked to further define clumps of of hair and minimal highlighs are added. The last brush size for the fur was a size 4.
Start with large, soft transparent brush and work toward a harder smaller brush. Except for the sketch, I only used the pen here. usually I would use a textured brush for shorter hair on the legs and face, but here I just use some of the textures for the legs. After all this I would merge the layers and clean up the outline with the eraser. Last step would be to add some stray hairs to the outline as well as some strong highlights.
The focus of the animal is the left side, so the right side has less texture to not distract from it. Less is more with fur and too much texture muddies up the whole image.