This achievement is story-based and cannot be missed. After you kill Hector there will be several cut-scenes and then achievement unlocks.

Hector can not be hurt by weapons. Once the fight begins, run to the back of the room to destroy his urn. Afterward, stand near one of the two columns in the middle of the room, wait until he attacks, roll away, so that he can smash the column. Let him destroy both columns to finish him off in this world.

His form in the Twilight World is also pretty easy. Attack his weak right leg until he falls, then keep hitting his back. Do this a few times and he will fall on his belly. Hit his head while carefully avoiding his bites and he will be finished quickly.