The term 'Billy Goats Gruff Foe' refers to the antagonist in the classic fairy tale, 'The Three Billy Goats Gruff'. The story follows three goats who must cross a bridge guarded by a TROLL in order to reach the lush grass on the other side. The TROLL is the main antagonist of the story and is referred to as the 'Billy Goats Gruff Foe'. The answer to the crossword puzzle is 'TROLL', which is a mythical creature often depicted as a giant, ugly humanoid with long hair and a beard.