This calculator will solve these kinds of questions:
Calculator to Find or Calculate Distance or Size of an Object in an Image
Essentially if I select the "Find the size of an object in Pixels" and plug in a size of 6-7 feet (wingspan if the eagle is grown and flying perpendicular to the camera) and I plug in 660' (1/8 mile) and I plug in various lens focal lengths I can determine the size of the object in my frame and then decide if I could crop and still retain enough detail.
Let's say we used 300, 420*, 560, and 784* (1.4x teleconverter) @660' and with a 6' target on an APSC 24mp sensor k-3 (4000 pixels high). We would get images of the following heights (in pixels):
300mm = 455 pixel height (a bit more than 1/10 the height of the frame...)
420mm = 636, still pretty small...
560mm = 848, less than1/4 the height of the frame but probably a crop could look nice enough.
784mm = 1187, just over 1/4 of the frame height. This seems viable cropped. It requires the DA 560 PLUS the 1.4x Teleconverter. And time and expertise and luck.