Simply kill 500 Enemies (Humans or animals, thanks to No121EIse for confirming that animals do in fact count) with any of the rifles or shotguns.
This achievement is cumulative of all weapons in this category, and should unlock right around the end of the single player campaign.
If (somehow) you have still not unlocked it after doing all SP activities, head over into multiplayer and grab kills there.
EDIT: It appears that Single Player and Multiplayer kills do not stack, so you must achieve 500 kills within one game mode. Therefore, if for some reason it didn't unlock during your SP run, the kills you earned there will NOT carry over to MP and you must start fresh. This rule also applies to ALL stats when going for achievements (i.e. pistol kills, animals slain, etc)
Rifles/Repeaters:
* Repeater Carbine
* Winchester Repeater
* Henry Repeater
* Evans Repeater
* Springfield Rifle
* Bolt Action Rifle
* Buffalo Rifle
* Rolling Block Rifle
* Carcano Rifle
Shotguns:
* Double-Barreled Shotgun
* Sawed-Off Shotgun
* Pump-Action Shotgun
* Semi-Auto Shotgun