You move with up, left, right, and not down because that's a different ability.
X is for attacking, Z is for melee, and down is for using a super ability.
A parry is performed when the enemy is close and you hit them with a melee attack; you'll obtain a piece of the Construct Star.
Once you have the entire Construct Star, you can use the super ability by pressing the DOWN key.
The new ability is the hammer that flattens enemies and is activated with C; it does not parry.