The Beast of Blue Rock lies within...the blue rock!
The Beast of Blue Rock is featured in the Fraggle Rock episode "The Beast of Blue Rock". The beast is not a physical creature but fear that surrounds the magical Blue Rock. As Marjory the Trash Heap explains: while the beast will return, with the help of friends it can be defeated -- as it was by Wembley and Gobo.
Marjory also explains that she was the one who made up the rumor of the Beast of Blue Rock, expressing surprise that the old rumors actually kept Fraggles away from the spot for centuries.