Great effort this, I am not sure what camera or lens you are using, however if you are able to do the following, IMHO this will assist in this type of shot.
You can keep the DOF as this looks ok, however you need to turn the auto focus to manual and focus in by hand.
Change the multi-segment to spot and as Huddersfieldhil says get the spot on the eye for sharpness.
BG is good, the FG twig and leaves will not completely go due to the closeness to the subject, however the above advice will make the bird pop from the image.
I hope you find this helpful.