Okay, below are first the "original", then my edit, and then your first edit. To really see the differences each should be viewed as the full sized version, but even the thumbnails show the obvious.

First, lets note that this is not an objective difference. Nobody necessarily need find any one of them to be the best, and somebody will like each best. This is just an example of what can be done, and of what I personally like best. Everyone's favorite is just a correct as the next!

I edited with GIMP. The first change was a slight crop to make the subject larger, retaining the 5:4 aspect ratio. I put the center just below the squirrel's lower jaw, half way horizontally between the eye and nose.

Then I increased contrast by 13 points. On the histogram that showed the maximum white level increasing a full stop from 231 to 249. The bump in the histogram at 208 moved up to 223 (almost a 1 stop change of 15 points). It lowered the black level sufficient that the histogram shows blocking at 0. The bump that was at a value of 32 dropped to 16.

Hence the shadows actually are blacker than "perfect", and the highlights 4 points above what I might think of as ideal.

I added "Sharpen" at 60% and UnSharp Mask with a radius of 3.0 and the amount set to 0.2. Values for sharpening do not translate well between editors, but the method to chose them was to view at 100% and allow just enough sharpening to see a change in the fur and whiskers around the mouth.