Wiktionary
n. (context science fiction derogatory English) An extraterrestrial.
Wikipedia
The bug-eyed monster is an early convention of the science fiction genre. Extraterrestrials in science fiction of the 1930s were often described (or pictured on covers of pulp magazines) as grotesque creatures with huge, oversized or compound eyes and a lust for women, blood or general destruction. The term is now often abbreviated to BEM.
In the contactee/ abductee mythology which grew up quickly beginning in 1952, the blond, blue-eyed, and friendly Nordic aliens of the 1950s were quickly replaced by small, unfriendly bug-eyed creatures, closely matching in many respects the pulp cover clichés of the 1930s which have remained the abductor norm since the 1960s.
Usage examples of "bug-eyed monster".
Oddly, there was no menace in it, probably because it was anything but a bug-eyed monster.
You didn't have to steal a little girl and turn her over to a-a bug-eyed monster!
It was done in garish colors -- a bug-eyed monster chasing a scantily clad female.