Lower, Mark A (1860) Patronymica Britannica: a dictionary of the family names of the United Kingdom. London: J.R. Smith. Public Domain.
ACHILLES
As described in historical dictionaries
Patronymica Britannica (1860)
ACHILLES. An ancient family of this name bore two lions rampant endorsed, probably with reference to the lion-like acts of the classical hei'o. Encyc. Herald. In the H.R. the name is written A Chillis.