“Lynx eyes” is an Spanish phrase (equivalent to "eagle eyes") that applies to a person of view particularly acute or especially clever and insightful understanding, ie. a crafty person.
We might think that the origin of the phrase is in the characteristic eyes of this animal, of the Felidae family and thus related to cats. The “lynx” has the bright eyes that appear to have a great insight and vision.
And yet that is not itself the origin of the phrase, although some connection there.
In Greek Mythology there are several characters that are called "Lynceus", on Greek Λυγκεὺς (Lynkeus). One of them is the son of Aphareus, king of Messenia and brother of Idas. The two brothers are part of the famous expedition of the Argonauts, that, led by Jason, goes in search of the "Golden Fleece".
Lynceus is famous for its extraordinary sight. Apollonius of Rhodes, author of the epic poem “Argonautica” ("The Journey of the Argonauts"), says exactly in the book I,151-155:
The sons of Aphareus, Lynceus and proud Idas, came from Arene, both exulting in their great strength; and Lynceus too excelled in keenest sight, if the report is true that that hero could easily direct his sight even beneath the earth.
And to confirm the statement of Apollonius, Pseudo Apollodorus says in his The Library (Bibliotheca) 3,10,3:
Aphareus and Arene, daughter of Oebalus, had sons Lynceus and Idas and Pisus; but according to many, Idas is said to have been gotten by Poseidon. Lynceus excelled in sharpness of sight, so that he could even see things underground.
So the phrase should really say " Lynceus eyes". But Lynceus is a little-known mythological character instead lynx is a beautiful animal predator of the feline family and related to cats. They live mainly in the northern regions, although there is a species in Spain, the Iberian lynx, Lynx pardinus, although endangered with a few hundred specimens. There is a major environmental program to ensure the survival of this animal.
Forgotten or little known the mythical carácter of the Argonaut, and best known the animal, it is easy to understand how the theft occurred because one of two things: either the bobcat (lynx) is named because it has Lynceus eyes or Lynceus is named because he has lynx eyes or lynx sight.
Because in any case, one must know that the word "Lynx" comes from Latin lynx and this in turn from the Greek λὺγξ. "Lynx" and "Lynceus" are obviously two words from the same root. So who really had Lynx eyes was Lynceus.
The Indo-European root * leuk is attested in many languages and means "bright". In Latin, for example, "luceo", clarify, clarify and "lux" "light". So probably this animal is called lynx by the brilliance of her eyes.
Some linguists relate the name λὺγξ , lynx, with the verb λεύσσω , archaic verb used only in the epic language meaning "look towards, to see." This relationship is possible and it would clarify the origin of these terms.
In any case it would be fair to speak of "Lynceus eyes or sight", but who is able at this point to correct language usage and custom of saying "lynx eyes"?
We will content ourselves at least advising the reading of the work by Apollonius of Rhodes "The journey of the Argonauts", the only epic poem after Homer to the Hellenistic period. Among other values of the work, it helps us to understand how the novel, literary genre more accepting today , came from the epic.