Kumubou's method is probably easiest; however, those wanting an alternate method can also meet Unlimited Ragna in Arcade mode.
Set the rounds to 1, difficulty to beginner, and time limit to infinite. Pick the character you're best with, and proceed to go through story mode like normal, making sure you win ten times by distortion finish. If you miss, or fail to finish off your opponent, let them beat up on you until you have less than 20% health, at which your heat guage will start to slowly decrease. That should give you one more opportunity to try again.
Once you defeat Nu, you should immediately proceed into a match with Unlimited Ragna. BE WARNED! He's no slouch, even on beginner! One of his distortion drives can nearly sap away all your health while fully restoring his, so do your best to stay away from him. Defeat him to pop the achievement.