Horse radical on the left supplies the original image: a horse rearing in fright. From that startled-animal scene the verb generalised to any kind of terror or alarm. Same radical anchors 驰 gallop, 骑 ride, 惊 (with a horse-component variant) startle.
Right side supplies the sound: hài → hài (exact match). 亥 is the 12th earthly branch in the calendar and carries no semantic weight in 骇 - pure phonetic. Same phonetic group includes 该, 孩, 咳 - all hài/gāi/hāi readings.
