When leveling up Yaiba, there's a perk in the bottom section of the skill tree called "Execution Chain" that allows you to execute up to 10 enemies in a row. Once you've unlocked this, simply surround yourself with a group of low level enemies, start swinging your chain (B), and you shouldn't have too much trouble getting a large group of them into Execution Status, where they have the "!" icon above their heads. Press LT to start the first execution, and you'll see a number of empty circles near the top of your screen that will fill with a green check mark when you've successfully committed another execution. You need to have no less than five of these appear, otherwise you won't have enough for the achievement.
To chain the executions together, you need to press LT again during the point in each execution animation where it goes into slow motion. If done right, you'll get another green check mark and you'll begin your next kill, resulting in a shiny new achievement once you start your fifth consecutive execution. If not done correctly, you'll get a big red 'X' for your effort and the execution chain will end. There are plenty of opportunities to get this, so if you miss one group, don't get frustrated... especially since manually restarting in this game takes you all the way back to the beginning of your current mission rather than your last checkpoint.
