Batman: Arkham Origins

This achievement does not have to be unlocked during predator challenges. I was able to get it by taking out two snipers who were by themselves on a roof during free roam. However, your best bet is probably going to be the predator challenges.

In order to do a silent takedown, you have to approach an enemy from behind without being spotted. Once you are right behind them, simply press Y like with any other takedown. Also, if an enemy is wearing armor, you cannot do a silent takedown on them.

In order to start the challenge maps, simply go to story mode and then select challenge mode. Select Batman, because it is still unconfirmed whether this achievement can be unlocked with Deathstroke. Then go to ranked challenges, go to the second page of maps and select the first predator map, "Breaking In."

Breaking In will be the easiest map to do this on, as there are plenty of gargoyles to use and there are only six enemies, all of which are unarmored. If you are spotted at any time during the challenge map, simply move between the gargoyles quickly and they'll lose sight of you. Also, dropping a smoke pellet is another good way to get silent takedowns. If a henchmen is in the smoke from your pellet, they'll panic and shoot randomly until the smoke clears. Simply crouch and move up close to them for the easy silent takedown.

If you have any suggestions on how I can improve this guide, please leave a comment.

This can easily be done while on your way to the south (third bomb) during during the mission involving Firefly on the bridge along with On your way there, you will come across 3 snipers looking over the railing with a viewpoint above each. Simply grapple to the first viewpoint and while their backs are turned, perform a Silent Takedown on the first sniper and grapple to the second and repeat. They are spread out enough that they will not notice the body or see you. After you take down the third, bam, two achievements. I got them on accident on the first try.

A 'Silent Takedown' is performed by approaching an armed guard from behind (usually while crouching), and tapping the Y button. Be careful not to press the X, as this will initiate a 'Knockout Takedown' which will not count as a 'Silent Takedown'.

To successfully pop this achievement, you have to finish a predator encounter using only 'Silent Takedowns'. This can be unlocked in either the main, core game or the challenge modes. You can be seen and shot at by the enemy and still not void the achievement. All that is required is that you do not neutralize any enemies with any other technique apart from the 'Silent Takedown'.

You'll know when you complete an encounter, as a XP scoring system will pop up to the right hand side of your screen listing the number you have taken down, and through what method.
Not confirmed, but I'm fairly certain you can also unlock this with Deathstroke.

I Did this accidently by grappling onto a roof with 2 snipers. One spotted me and i used a smoke pellet to evade him, crawled behind him and did a silent takedown.

Then i crouched to the other one and did a silent takedown on this one too and click... Achievement unlocked. So if spotted on The roof simply use a smoke pellet, this will be a big help! :)

Happy hunting!