Hi Paul,
Your image proved to be a little tougher than I had expected, there were some areas where the shadow details were a little off, parts of them were greenish looking, not sure what the cause could be though.
I tried to raise the exposure level of both the sky and the osprey pair while keeping an eye on how well they blend together visually and it seemed to work fairly well.
The feathers on the male was a challenge because there were small areas that were darker than others, some areas were even a little off with color, maybe the male was just dirty and needed to bathe before getting dirty 
The sky worked out fairly well in my opinion, I was able to use a mask created with a brush set at about 50% density, 50% flow, 75% feather with the brush size at about the diameter of the female osprey’s body and wings, then I brushed little areas of the sky randomly with the blacks, exposure and shadows raised a fair amount, this in essence raised some highlights and even created some whitish clouds, then I adjusted the amount with the amount slider to fine tune the effect.
Then on the nest I created individual masks using a small brush about the diameter of one twig, I created a mask for each type of twig, one for the brown ones, one for the green ones, one for the moss and one for the shaded underside, then I adjusted them to make the browns more brown using various saturation, exposure and even temperature and tint sliders, then made the greens greener, etc.
I did the same process on the branches to bring out more of the details and color.
The main takeaway is to target very small portions on each element with individual masks, then work on blending them all together using the “Amount Slider” in the mask section.
BTW, I used Lightroom for all of the adjustments, I stayed in the masking section most of the time but I did do some minor tweaks in the global section.
Another takeaway is to make all of the adjustments in small amounts at a time while keeping a copy of the original open a separate window for comparison (I use the photo viewer for that part).
I might have been able to g et it better if I had spent more time on it. As it stands, I spent about 2 hours on it and the results are somewhat acceptable (I think?) You should be the judge of that
The raw file might have been much better in regards to the shadow details but I’m not familiar with your specific camera, and it could be that the jpeg file compression was the cause of that issue.
Also, it is good that you shot this slightly under exposed! It’s always easier to correct for exposure in post processing. The feathers on the belly of the male was very near to being over exposed even being shot under exposed, so, don’t change that practice while shooting IMHO.
I’m sure you can do much better with the raw file, just take your time with it and take a break away from it periodically, it might help (it helps me when I do that).
Anyway, I think it’s a great image!
I like the composition of this and I think your choice of cropping the bottom where you did was a good one, The branch going off to the left at the bottom wasn’t very appealing or supportive IMHO.
But, I think @Mike_Friel’s suggestion for cropping off the nest was also good but you would need to crop some off the left too just to keep the action in the center horizontally, maybe crop just a tad off the top as well to keep the action in the top third of the frame vertically.
Thanks for letting me work on this.
Have a great day!
Original Version:
Edited Version Below:
edited Version with Optional Crop Below:
