Hold LS towards a new enemy as soon as your counter kill starts, and then hit x as the kill ends. It's quite fluid, try not to button mash too much, it just needs a bit of timing.
Also, I'm pretty bad at chain kills, and I only got the achievement by using the dagger. You can hold down x instead of tapping it when you go in for you instant kill, and you'll kill two people at once - one with the dagger, one with the hidden blade.
Check out this tutorial
, it helped me