The crossword solutions for the term 'RUN LIKE BILLY-O' are TEAR. This phrase is a reference to the character Billy-O, a character from the popular children's book series The Magic Tree House. Billy-O is known for his incredible speed and agility, and the phrase 'run like Billy-O' is used to describe someone who runs very quickly. Therefore, the solution to the crossword is TEAR, which is a synonym for running quickly.