This achievement requires you shoot 10 Monobeasts in a row without missing, which is very tricky: not only are Monobeasts tricky to find, but shooting 10 in a row without missing can be infuriating.
Monobeasts very rarely appear without some sort of interaction. If you pause the game and move furniture, you can find them hiding underneath. I found I had greater success looking underneath vending machines, arcade machines, water fountains and even newsagents.
I would play through the game as you normally would for a few hours, completing objectives on each stage. Then revisit a more established hospital that you've had for a while and begin lifting furniture. More often than not, you'll find Monobeasts in large groups which makes earning this achievement easier. If you have a dirty hospital with few janitors, even better.
To earn 10 kills without missing can be made easier by first pausing the game (space bar), lifting the furniture to uncover the little bastards, placing the furniture out of the way, trying to predict the path of a single Monobeast (they usually follow the path they're facing), lining up the shot, unpausing the game (space) and then making the shot. You'll then need to do this 9 more times without missing; if you miss, you've got to do it again from scratch.
For every shot you succeed with, a counter will appear next to the deceased Monobeast for easier tracking.