Bombs are unlocked after memory five. They can be selected like any other weapon from the hand menu. You can throw bombs if you press the bomb button while running, or lay them in a set spot if you press the bomb button while standing.
I found it easiest to kill the sleeping or unaware guards for this achievement. Anytime you would normally use the finger blade to get an instant kill, you can instead lay a bomb at the feet of your enemy and walk away letting the bomb explode.
Note that if you happen to die before a checkpoint and the game auto reloads your last checkpoint, you will lose any progress you made towards this achievement since your last saved checkpoint.