Although the pop-up text shows "Crushing Hit" when it happens during combat, the in-game help describes crushing hits as "Fatal Blow" -

"Fatal Blow - Attacks with a fatal blow with a fixed chance if you don't get a critical hit when attacking with an advantageous attribute. The fatal blow inflicts 30% additional damage."

So we basically have a list of various types of hits that can occur:

  • Glancing hit: 30% less
  • Normal hit: 0% additional
  • Crushing hit: 30% additional
  • Critical hit: starts at 50% additional and goes up according to your Crit DMG value

See also: Hit Table

The most common situation when you might get a crushing hit is when you are attacking with attribute advantage. This will give you a small chance to crush; but it still won't happen if you got a glancing hit instead, or a critical hit instead. (This is most famously the case with Ifrit (Water) - Theomars. While his passive grants him attribute advantage whenever he attacks, he won't get a crushing hit if he gets a critical hit instead. And critical hits are much more damage than crushing hits, so, that's a good thing.)

However, several monsters have a skill that guarantees a crushing hit. They include language similar to "This attack always lands as a Crushing Hit regardless of the enemy's attribute." These attacks absolutely will never glance, never crit. They will only crush!

Arguably, the primary benefit of a guaranteed crushing hit is the prevention of a glancing hit, because glancing hits cannot apply debuffs. Note, then, that another way to prevent glancing hits is to use an attack which deals no damage at all, since it is not a "hit" of any sort.