As you attack things you'll notice a multiplier appear under your health, this is the multiplier the achievement is referencing. The max is 5. Early on when enemies die easily this is fairly hard to accomplish, if you want it out of the way early you'll need to chain a bunch of attacks on an elite or a stage end boss. Later on enemies take a lot more damage, and X5's become pretty common. Using combat arts seems to increase the multiplier faster. I believe most people will have this without trying before they finish the game.