The subject seems to me was stationary. Even so I tend to shoot continuous firing but keep AF-S as my main focus modality with the center sensor selected. This has worked for me.
We all know that the aperture in use is important because even at great magnifications we always have the advantage of some depth of field. A high ISO setting is a must to allow a high shutter speed in conditions like this when it is cloudy and windy.
The exposure was off, I do not believe I have to comment on that. The first shot is easily 1.5 stop underexposure. The others are also underexpose. Editing programs can improve on that exposure using curves and some sharpening to improve on the quality of the photograph. I tend to use selective sharpening also when in need although I am not aggressive using it.
I used the third shot to do what I would have done in post with my image. I used Photoshop and I hope the gentleman who is the original poster will not mind my intrusion. I am only trying to help.
I am sure Mr. Perry will be the first one to tell you that most AF problems are operator's problems. When I am using AF with lenses that have IS or VR, I wait a second after I achieve focus to snap the shot. That gives the IS or VR a chance to stabilize the image. That is what I have done for years and it seems to work very well for me. Obviously, I am talking about stationary subjects.
You have gotten excellent advise for your inquires from other members so I believe that using those advises at your next shooting should improve on your technique...and make sure the histogram in camera shows a good exposure.

I was able to find a snow owl to shoot yesterday and he was pretty sedentary even with folks coming and going to get his Photo. I used my D7100 with a Sigma 150-600 on a monopod stabilazation active because of the high winds, with the Iso up a bit to keep the Shutter speed up and because of the grass blowing right in front of his face, I used his front shoulder as my focus point. It just doesn't seem as sharp as it should be. I also shot with my D600, Nikon 80-200, 2.8 with a 2x converter and no stabilazition and had about the same result. Then I tried with the 600 and the Sigma and basically got the same result. I used his shoulder for my focus point in each photo. It was late afternoon and overcast. Am I expecting to much or is there something I could try for a better result?
Thanks for your informed replies.

I was able to find a snow owl to shoot yesterday and he was pretty sedentary even with folks coming and going to get his Photo. I used my D7100 with a Sigma 150-600 on a monopod stabilazation active because of the high winds, with the Iso up a bit to keep the Shutter speed up and because of the grass blowing right in front of his face, I used his front shoulder as my focus point. It just doesn't seem as sharp as it should be. I also shot with my D600, Nikon 80-200, 2.8 with a 2x converter and no stabilazition and had about the same result. Then I tried with the 600 and the Sigma and basically got the same result. I used his shoulder for my focus point in each photo. It was late afternoon and overcast. Am I expecting to much or is there something I could try for a better result?
Thanks for your informed replies.