The Soul-catcher is the Silver gun that Death gives you at the start of the game. You will start of with a shotgun and the Soul-catcher. It fires spinning blades in its primary state and reaps souls with its secondary fire mode. Both of which count towards this achievement.
This is likely going to be achieved through natural progression of the storyline (As you have to complete it a minimum of 2 times for all achievements) as well as completing the 1000 kills for survival.
However, if you do want or need to grind this out for any reason, load up any survival map of your choice and set the "Kill" and "Time" limit to appropriate lengths; then simply start the game and begin killing. You spawn with this gun in Campaign AND Survival every time. Ammo comes in the silvery spheres that you can find lying around in every map.
It is really effective at clearing rows and lines of enemies. Especially if you aim it at the head, as it can slice multiple heads off if the enemies are aligned. For this reason, it's quite good on the first level where you can decapitate lines of skeletons easily. It's also reasonably good at killing shielded enemies like the templars because you can aim at their feet and it will slice them off, providing an insta-kill for you and a hassle free method of getting rid of these annoying foes.