Are you trying to detect nearby gunshots (like a range counter) or something like Shotspotter that detects them in a neighborhood setting? The first seems far easier to me and what I would be doing is getting a commercial range counter and - read with an Australian accent - TAKE IT APART! I don't see why Arduino would not be up to this application as a range counter gunshot detector - I think the processors used on those are probably inferior to the ATMega328. If it is more like Shotspotter where you are trying to pick it out of a cacophony of noise, I think Arduino is also a poor choice.
TAKE IT APART!
![DaveHand350x350[1].jpg](https://europe1.discourse-cdn.com/arduino/original/2X/9/91b1f691393bf0f787a80e8e10749d1e77c25078.jpg)