Control Points act as the fast travel points throughout the Bureau, as well as allowing you to access your countermeasures and sort out your upgrades.
All Control Points have to be either 'claimed' or 'cleansed' to be used. Only cleansed Control Points count towards the achievement. Control Points that need to be cleansed glow red, and cleansing them often alters the environment around you. This achievement will come during natural gameplay, as you are required to cleanse more than 10 Control Points to progress the story and open up previously inaccessible parts of the Bureau.
To cleanse a control point, walk up to it and hold
. There will be Hiss around corrupted Control Points, so they will need to be eliminated before you can cleanse the Control Point.