Just finished a commission piece with a carved animal head on the front panel and I figured I'd share what finally made my portraits look right, because my first five attempts were honestly terrible. The biggest mistake I made early on was tracing the outline and jumping straight to beveling. What actually works is doing a light swivel knife pass first, then coming back with a modeling spoon to push the background down before you ever touch the beveler. The relief pops way more when the recessed area is smooth and shaded instead of just cut around. Hair texture is where most people give up. Don't try to cut every strand, it looks stiff and weird. Use a hair blade or even a small veiner and work in the direction the fur grows, in short overlapping strokes. Follow the muscle underneath the fur, not just the outline. A cow or bull has that big hump over the shoulders and heavy folds at the neck, and if you model those first with a spoon, the fur strokes practically lay themselves out.
One more thing, dampness. I used to case the leather til it was dark and soggy, and my fine lines came out mushy. Try tooling when the leather returns to its natural color on the surface but still feels cool underneath. You get crisp bevels and the fine detail work holds an edge. Sketch the animal a dozen times on paper first too. If your hand doesn't know the shape, no amount of tooling will save it.