A great way to grind this (and all the other kill x enemies with y weapon achievements) is in the Memorial Gardens chapter. In this level you will fight a Ghost boss 3 separate times. During these battles, DO NOT KILL THE GHOST. So long as the ghost is alive, it will keep spawning enemies and you can just mow them down with the weapon of your choosing. There is a limit however, and it will stop spawning enemies after maybe 50 or so are killed. Since there are 3 battles you have around 150 enemies in this level to kill.
I'm don't know if achievement counters carry over to a new game, but I do know that you can just load up any level from the main menu and your counters will still be in the same spot. I needed 3 more environmental kills and 4 more tear kills to get those achievements and my counter didn't reset even though I had finished the game.
So long as you focus on using weapons that you need achievements for while you are playing through the game and grind the ghost boss; you should have no issue getting all the kill related achievements in one playthrough.
As always, if you vote negative, please tell me why so I can improve my guide. :D