In this video guide I will show you how to use the Brain Crush on Others 20 times. You will eventually be given a tutorial on how to do brain crush. You need to drain the crush bar which is the yellow bar beneath the health bar. Once it's depleted you use LT to finish them off.
A really easy way to get the bar down faster is to use Kagero. Use his invisibility ability and get close to the enemy and hold the Y button. This will take away a good chuck of the bar. Then just use psychokinesis to throw some objects to finish the bar of and a brain crush to finish the enemy.
A few skills that help out are: brain crush chance expand and psychokinesis crush effect up. Once you get the twentieth brain crush the achievement will pop.