I have searched a long time to find just one word that can describe these birds when they are truly in hunting mode. I believe intensity covers it all, as it does for everything found in nature.
Intensity, as defined in the Merriam-Webster online dictionary
1: the quality or state of being intense; especially : extreme degree of strength, force, energy, or feeling
2: the magnitude of a quantity (as force or energy) per unit (as of area, charge, mass, or time)