Hi there,
You'll probably run into a level that you'll fail at least 10 times before beating it.So it will come through natural gameplay.
If you want to get this achievement out of the way immediately, here's how to do it:
Start the game. Go to the tutorial. The first thing you encounter is a circular saw. Just run into it 10 times and that should do the trick.
I have heard of people not getting this achievement in the tutorial. So, here's option 2:
Load up the first 'real' level after the tutorial. You start at the top of a wall with an enemy patrolling around at the bottom of said wall. Just drop down and let the enemy kill you 10 times.
There you go. An easy 33 GS
Cheers!