Big How do you do it? Your hand holding monster lenses and monster cameras!
Its a great shot i must say, i m not such a big bird fan, but this is a good photograph. Was it cropped from the start?
...... elbows tucked in tight, relax, control breathing, have camera set on continuous, pan with subject with a gentle touch of the shutter for a burst of exposure's....... and yes the gear does get heavy but also helps with steady and controlled movement
EDIT: and many years of practice
no cropping full frame image