What is the medical term meaning fast difficult breathing?

Tachypnea (tachy = fast + pnea = air) is breathing too fast and shallow.

Hyperventilation (hyper = a lot + ventilation = breathing) is rapid, deep breaths because of anxiety or panic.

Dyspnea (dys = difficult + pnea = air) is when taking a breath brings on discomfort.

Dyspnea is a symptom. Tachypnea/hyperventilation are signs.