"breathe deeply and rapidly," 1931, from hyper- "over, exceedingly, to excess" + ventilate in a medical sense. Perhaps a back-formation from ventilation. Earlier in a transitive sense, "to ventilate thoroughly" (1920 of lungs, 1906 of rooms). Related: Hyperventilated; hyperventilating.
The nurses had to hyperventilate the patient
The mountain climber started to hyperventilate
hypertext
hyperthermia
hyperthyroidism
hypertonic
hypertrophy
hyperventilate
hyperventilation
hypervigilance
hypha
hyphen
hyphenate