Mermaid
Reference: Mermaid
Passes the limb test and fails a different one. Two arms and a fused hind limb pair is a legal count — the problem is breathing.
Scored on every axis
Legal limbs, impossible lungs
Counting limbs, the mermaid is fine: two forelimbs as arms, the hind pair fused into a tail. Whales and dolphins did something structurally comparable, and kept a vestigial pelvis while doing it. Nothing here violates the four-limb constraint.
The respiration axis is where it fails. A human upper body has lungs and no gills; a permanently submerged lower body needs oxygen extracted from water. No vertebrate has ever re-evolved gills after losing them — whales went back to the sea and still surface to breathe, after fifty million years of trying nothing else.
Nor can a body run half on each. Gills need continuous water flow across a large thin surface; lungs need that surface kept dry. The two requirements are directly opposed, and there is no arrangement that satisfies both in one animal.