While you're in New Orleans (about halfway through the game), you'll run into a man called Horton (make sure you have as much health and armor as possible before trying this). After a long cutscene with him, you'll be riding a Panzerhund, the giant mechanical dogs that breath fire. Make sure you're playing on "Bring 'em On!" and simply run past everything (I'd also recommend making a manual save as soon as you start).
All you have to do is ignore the enemies and keep running forward (the sprint button still works). Be sure to steer clear of enemies, because the Panzerhund can kill enemies by stepping on them if you're not careful. You have limited armor, but you can get some more by smashing into crates off to the side of your path. Your Panzerhund likely won't survive the whole trip, but when it dies, you can just get off and keep running past enemies. Eventually, you'll wind up in the sewers, so just keep running toward the objective markers and until the achievement pops.
It may be possible to play the majority of this section on the lowest difficulty and switch to Bring 'em On! at the end, but I can't confirm this (If you can, let me know and I'll edit).
EDIT: I'm being told that only kills while on the Panzerhund count. Once you get off, you're free to kill to your heart's content.
Also, if you miss this, you can play on the easiest difficulty up until you get to Horton (and grab his hand to end the level) and switch to Bring 'em On! right before starting the next level.