A Barrier Burst is activated by hitting all of the face buttons on an Xbox controller, or the J, K, L and N keys on the keyboard. Doing so will cause you to Barrier Burst. A Barrier Burst can be done once per round. Once you Barrier Burst you'll be put in a "Danger state" in which you take 1.5x more damage than normal.
This achievement can be obtained in Versus Mode or whilst you're going for "NOT BAD AT ALL!!" It's best if you go for this achievement whilst doing the arcade mode achievements, simply beat your opponents to low health, then proceed to Barrier Burst before delivering the finishing blow. Once you Barrier Burst finish off your opponent.
If you choose to do this in Versus Mode due to having a wired controller, change the settings to:
Number of Rounds (Versus): 5
Time Limit (Versus): 99 seconds
Select Jin Kisaragi as your character. As soon as the round starts, barrier burst by hitting +++ and finish off your opponent. Keep repeating until the achievement unlocks.