Go After Flies is a phrase used to describe the act of trying to catch or kill flies. The two crossword solutions for this phrase are SHAG and SWAT. SHAG is an informal verb meaning to vigorously shake or move something, which can be used to describe the motion of trying to catch a fly. SWAT is an acronym for Special Weapons and Tactics, which is a term used to describe a police unit that uses specialized weapons and tactics to apprehend suspects.