Sphinx

The Sphinx (Σφίγγα in Ancient Greek), also known as "The Master of Riddles," is a creature with the head of a woman and the body of a lion.

History
The Sphinx is said to have guarded the entrance to the Greek city of Thebes, and to have asked a riddle of travelers to allow them passage. The exact riddle asked by the Sphinx was not specified by early tellers of the stories, and was not standardized as the one given below until late in Greek history.

It was said in late lore that Hera or Ares sent the Sphinx from her Ethiopian homeland (the Greeks always remembered the foreign origin of the Sphinx) to Thebes in Greece where she asks all passers-by the most famous riddle in history: “Which creature in the morning goes on four legs, at mid-day on two, and in the evening upon three, and the more legs it has, the weaker it be?” She strangled and devoured anyone unable to answer. Oedipus solved the riddle by answering: Man—who crawls on all fours as a baby, then walks on two feet as an adult, and then walks with a cane in old age. By some accounts (but much more rarely), there was a second riddle: "There are two sisters: one gives birth to the other and she, in turn, gives birth to the first." The answer is "day and night" (both words are feminine in Greek).

Bested at last, the tale continues, the Sphinx then threw herself from her high rock and died. An alternative version tells that she devoured herself. Thus Oedipus can be recognized as a "liminal" or threshold figure, helping affect the transition between the old religious practices, represented by the death of the Sphinx, and the rise of the new, Olympian gods.

Tips for Demigods
Fighting a sphinx is nearly impossible, and will get you and any number of your companions killed. Your safest bet is to answer the riddle, or whatever questions it asks you.