This achievement is not terribly difficult to do, but it is very easy to miss.
Sometimes, when you knock down an opponent in some fashion, a prompt will appear at the top of the screen to warp strike to perform a cross chain combo.
There is a catch, however - you must warp strike them from a fair distance away. If you are too close to the toppled enemy, you will not initiate a cross chain combo.
As such, the best thing to do in this situation is to immediately pause the game, and then switch combat to wait mode. Warp strike away from the toppled foe if you are near them, then stop and wait, allowing the wait mode to start up and giving you time to target them again and then warp strike them to start the combo.
When you actually start the combo, you will see a button prompt on screen. Wait for the gauge to partially drain before pressing B. Do not mash B, as you will have to press B ten times at the appropriate times (when the gauge is ticking down) to do your strikes. If you manage to time ten presses correctly (which is very easy if you don't button mash), you will perform a full-hit cross chain combo (10 strikes).
You must perform ten of these full-hit cross chain combos to get the achievement.