Hyper Dying Will Mode (probably known as something fucking retarded as "Hyper Deathperation" in the Viz Media localization) is the successor transformation to Dying Will Mode introduced in Katekyo Hitman Reborn as well as appearing in Neo Scary Godmother.
This transformation is activated when a user is either hit with the Rebuke Bullet, or can similarly ingest two Dying Will Pills, however the latter won't be as strong. Those who have full mastery over the form can simply will the transformation on command.
Unlike the previous form, Hyper Dying Will instead removes internal limiters in the body, releasing the users hidden awareness. In the case of those carrying the Vongola bloodline, this transformation is the catalyst for awakening Hyper Intuition.
Energy consumption and stamina depletion is greatly reduced as opposed to Dying Will Mode, since this form uses dying will in reserves as opposed to expending a lot of power at once. Also of note, the clothes remain intact when transforming.