This achievement can be obtained immediately upon picking up the Altered Biocell for the "Retrieve The Package" sidequest (you can find the required door code in the showers, inside the teddy in the garbage can to your left; it's 6014). If you want the achievement as fast as possible, you can immediately use the Altered Biocell, which will grant you access to your augmentations. In order to do so, just open your inventory, highlight the item, press
to use it, and unlock the achievement. If you're going for the "Winners Don't Use Drugs (or Biocells)" achievement, save your game before consuming the Altered Biocell and reload it afterwards, otherwise you're screwed out of that achievement.
I'm not sure how long it would take to obtain the achievement by bringing the Altered Biocell to Flossy in cell A-212, as I unlocked it by consuming it.