If you would like to get this quickly you will need 40 Spare Parts, and Repair III.
If you need more Spare Parts you can't craft them, however you can unlock the Dismantle skill, which will allow you to dismantle weapons for Spare Parts. With this you can craft a weapon (such as a Wrench) at a Fabricator and dismantle it to get spare parts.
You must do this in one playthrough, but you can repair the same item repeatedly. Simply find a turret and hit it with your wrench until it is broken, then repair it. Repeat this 20 times to unlock the achievement.
A good spot to do this is right outside your own office, there is a turret there as well as a Recycler and Fabricator very close by.
You can quicksave before beginning if you don't want to waste your Spare Parts or Fabricaton materials.