This is one of the most annoyingly difficult achievements in this DLC / Main version of this game.
This should be done under the upstairs balcony, close to the table, as it helps with the initial stacking.
I believe you can stack 3 stools on top of each other. From there, you have to climb on top of another stool and place 1 - 2 more on top of it. Once you've got the initial 4 - 5 stools stacked under the balcony (as straight as you can get them), SAVE THE GAME! From there, take the rest of the stools upstairs and (meditate like a monk) as you climb on top of a stool and drop stools over the balcony, onto the tower. Reload when it inevitably falls, until you eventually get it high enough that you don't need to stand on a stool to reach over the balcony. From there, stack the last 1 - 2 ontop of the pile.
Make sure it stands on its own and isn't leaning against the balcony, as this won't count.