Complete the following main story quests to unlock this quest and then complete it to unlock the achievement:
Dragon Rising*** Spoiler - click to reveal ***This mission immediately triggers after you complete Bleak Falls Barrow. You will have to accompany Irileth and a bunch of guards to the Western Watchtower (south west of Whiterun) on a dragon hunt. Once Milmunir is down, you have to stand around its corpse to absorb his soul before returning to tell Jarl Balgruuf the good news.
The Way of the Voice*** Spoiler - click to reveal ***Starts right when you finish Dragon Rising. You must first travel to Ivarstead, south-east of Whiterun (east of the mountains). From here, walk the 7000 steps up the mountain to reach High Hrothgar. Talk to Arngeir of the Greybeards there. He will ask for a demonstration of your shout and will then teach you a new technique. When the lessons are over, the trophy should pop.