The phrase '飛ぶ鳥を落とす勢い' always reminds me of those epic battle scenes in 'Attack on Titan' where Levi moves with such blinding speed that you can barely track his movements. In English, we'd probably say 'with the force to knock birds out of the sky' or more dramatically 'with earth-shattering momentum.'
Interestingly, this concept appears in Western media too - like when Thor's hammer strike in 'Avengers: Infinity War' had enough power to stagger a giant spaceship. The English language tends to favor hyperbole for these situations, using phrases like 'unstoppable force' or 'enough power to bring down the heavens.' Each culture has its own colorful way of describing overwhelming power.