During memory 5 of sequence 3, you'll come across a plantation that has guards and alarm bells. Smelling the achievement, I let the alarm bell guard notice me and ring the bell, I shot him as he was ringing the bell.
No achievement. Huh.
After a few reloads and still no luck, I figured it might be that I had to actually perform an assassination... so next reload I did a running assassination (hold RT and X at the same time while you have swords or hidden blades activated) on the guard.
Others have confirmed that the achievement will pop as long as you're assassinating your target. Getting in a fight before you kill him doesn't count and using guns doesn't count either.