On Mission 08: Demon King, there are two lava walls which repeatedly generate platforms that rise up. In the second of these areas, there is a platform off to the right that Nero can jump to. From here, use the Grim Grips to reach the area with the Secret Mission.
The goal of this Secret Mission is to use Grim Grips to reach the Blue Orb Fragment without touching the ground. The spacing of the Grim Grips is such that Nero does not require any unlockable air moves to complete this secret mission, though having Air Hike and Calibur certainly helps. Melee attacks in mid-air can be used to increase Nero's air time if the player is having trouble.
The Grim Grips each require a shot from Blue Rose before Nero can grapple onto them, so get used to a rhythm of shooting and then grappling quickly. Make sure to pay attention to the UI and how the camera behaves - once the target is locked on, the camera will focus on it quickly and the lock on circle will appear around it. If it is not locked on, the camera will keep panning and following Nero's movements rather than the target's movement.
Riding Punch Line also does not count as touching the ground, and this can be used to skip sections of the course.