This is one of the first achievements you'll earn in the game. In Mission 1: Found, Dante is pursued by a giant demon known as the Hunter. At the end of the level, you'll be forced to fight it.
The Hunter attacks quickly, so make sure to dodge a lot. Once he starts spewing fog, he'll throw his knife at you, so be ready to dodge.
Taking the Hunter down is rather easy; jump up to his face and attack him until he gets dazed. Attack him more to make him fall down to the ground, and deal some final damage to finish him off. If you manage to do this in a flashy way, you'll be able to also unlock the "Sensational!" achievement, which is unlocked by preforming an SSS Style rank combo.
You can also watch the video below. All credit for the recorded footage goes to Mr. VG247.