This achievement is misleading. You must cancel a critical counter from the other opponent in vs. or online. This is best done with a light punch or light kick (crouching light kicks worked best for me) in versus with a second controller.
In versus, use a second controller and use that second character to damage your 1st character until the green gauge below their life bar is full (the critical counter gauge). When the critical counter gauge is full, use the button the initiates the critical counter (for most characters it is hard punch, but for others, i.e. Kim, it's hard kick) - you'll know as it second character will have a glowing punch or kick after the gauge is full and slowly draining.
When you initiate the critical counter with your second character, immediately hit light punch/kick with your 1st character to cancel/prevent the critical counter from occurring. Repeat 10 times and this should unlock.
Credit to Moon_Child79 & DashmanX at x360a.org.