Its Gatling Gun can be fairly devastating and can easily wipe out even Snow with 1,400 HP. The Falco Velocycle will begin charging for Gatling Gun when its stagger gauge is approximately 60-70% full, but Gatling Gun's charge will be canceled if the enemy is staggered before it releases its attack.
The player should change paradigms to Building Block or Lifeguard and have Snow use Provoke, followed by Steelguard. If done fast enough, this will minimize the damage received. However, with the party consisting of Lightning and Hope, as soon as Falco Velocycle is about to use Gatling Gun, the player should switch to either Medic and Medic, or Medic and Commando/Ravager. As a last resort, the player can summon their Eidolon as soon as Falco Velocycle uses Gatling Gun.
Alternatively, one can start off with Slash & Burn (COM/RAV), to get a few hits in with Commando to ensure the stagger gauge doesn't drop too quickly, then attack all out with Dualcasting (RAV/RAV) and try to cancel the Gatling Gun by staggering Falco Velocycle during its charging period.
Equipping the party such to synthesize the Physical Wall bonus will also drastically reduce the damage received.
Falco is Latin for "falcon".