A mechanic that was first introduced in the Thousand Year Old Door is called "Stylish Moves", which requires skill but grants your attacks more damage.
Here's how to do more damage with your attacks by executing a Stylish Move in Paper Mario The Origami King.
How To Do A Stylish Move In Paper Mario The Origami King
Jump: Tap A at the peak of each arch after stomping on your foe. If you perform the second jump, you can perform a second stylish move by tapping A on the way down. Ultimately tapping A three times at the right time will earn you two attacks and two stylish moves.
Hammer: Tap A just has the hammer hits your foe, and again when Mario touches the ground.
A stylish move can be done with both with a jump and hammer. In some occasions, you may also be able to do them with your partner.