The Sanatorium is a Dome Spire building gained from the "Behavioral Shaping" research tech in the Social tree.
Once you've researched the technology, build a dome and place the Sanatorium in the middle. To make things go faster, build an oval dome and put the Sanatorium in with the Arcology in order to maximize the population you can treat. Otherwise, build a few apartment buildings such that the total capacity of the dome is greater than 50 (not required, but helps to speed things up if colonists don't have to constantly move between domes).
For the Sanatorium itself, activate all work shifts and then select the Flaws you wish to correct. I selected Lazy, Alcoholic, and Gambler, since I saw those having the largest impact on my work force. Once you've done this, for the dome that has the Sanatorium, select the Dome, hit
to select the infopane, hit
to select "Filter by Trait," and open that menu. Go down to the Flaws sub-menu and approve (thumbs up) the three flaws you specified in the Sanatorium menu. Hit
to go back to the main filter menu, then hit
Now, go to each other dome you have (if applicable) and do the opposite - disprove (thumbs down) those traits and apply. That will encourage colonists with those traits to relocate to the dome with the Sanatorium.
After that, it's simply a waiting game. It took about 10-15 Sols for my achievement to pop. You can monitor the number of colonists who have been "cured" of negative traits by select the Sanatorium ("Lifetime cured").
Edit (5 Apr 2018) - An upcoming patch
will allow colonists to be directly assigned to the Sanatorium for treatment. This should help speed up progress toward the achievement. In my opinion, though, with so many other things to do, passively treating colonists will be the simplest way of getting this achievement.
Edit 2 (8 May 2018) - With the introduction of Passages, this achievement should be even easier to get, as you can link together domes now and they'll share populations and services.