There is a very simple way to earn this quickly pretty early on in the game. Make sure you have unlocked the first hacking skill so that you can hack level 1 items. Once you have the skill go to the Hardware Labs(You go here in the main story during the quest Through a Glass Darkly).
Once in the Hardware Labs there is a room off to the right of the Atrium called the Ballistics Lab(If you need help finding these you can download the area map at the security terminal at the start of this area).
You'll need the keycard to get into the labs, but luckily it is on the body directly to the left of the door. Once you enter the ballistics lab turn right and there should be a safe that you can hack in the corner. Just hack the safe and once finished lock the safe using the button and hack it again. Repeat this 20 times and the achievement will unlock.
Edit: I'm pretty sure you can re-lock any safe, so it might not have to be the one in the ballistics labs. That's just the one I did it on.