This arises out of Frank's question over in the POTD thread.
It's certainly possible to tweak it in PS but it won't be the same as getting it right in camera; you can't put back the shadow detail that was lost and the underexposure begets a noisier image as well.
You can see that the Osprey pixels are all concentrated into the bottom two thirds of the histogram, the top third is all the lighter pixels of the sky and you can clearly see the clipped shadow detail in the "wall" of pixels at the left.
In this screen shot you can see I've dragged the slider way left of the sky pixels. This brings out more detail in the Osprey whilst the sky is totally demolished and some highlights on the bird blow out.
With the layer mask active on the levels adjustment layer, using a black brush and 20% opacity we can paint the detail back into the bird. Do the same at 100% to the sky.
And that's about it apart from using a hue/sat adjustment on the sky. The detail is improved but nothing can be done about the clipped shadow detail which is gone for ever. This process should work better on the original image than on this low res one.
Before and After (or rather after and before).