Dying Light

A tip about Volatiles is that they can't swim. They die instantly if they go into water.

So I made a quick guide showing how I unlocked my achievement.

Be aware, there are actually 3 Volatiles in the cave but I had already killed the other two in the same way.

(Upload Studio doesn't show achievements popping up, so it won't show up in video)

I don't think my way is better than Ryan's but it's how I did it and thought it may help someone out.
Basically when you notice night is almost at an end, find a volatile. As soon as night is over they start getting burnt by the sun and run. Just chase one, throw stuff at it and as soon as you are close enough slash at it. They are very fast, but easy to follow as they are glowing. I got it first time I thought of it and tried it.

Fence Trap solution
Volatiles only come out at night and are displayed on the mini-map. They are extremely hard to take down with standard weapons so the use of traps makes this a lot easier.

The Tower from the beginning has electricity traps at the entrances and they can be activated when you stand next to them. Look for a Volatile next to the tower and make him chase you back to the trap. They sometimes back off if you are to close to the entrance. As soon as one comes up activate the trap and do additional damage with grenades, molotovs, throwing stars,...
The trap alone won't kill it mos likely.

This method worked for me, and I got my first kill on the first night during the drop mission...

Just south of the tower is a sage house that's beside an apartment block, the way in is through a hole in the roof, for the setup make sure that you have the UV light as your "thrown weapon" as this costs nothing and does damage

Opening the door and wandering in the "fenced" area starts attracting the volatiles, but if needs be jump onto the roof and wander around, once one is near you drop down and enter the door, the volatile will walk in and stop at the door, use your UV light to burn them and if you want to do this slow just stand inside and they won't enter while you're burning them, to speed this up you'll use some resources but hitting them with melee will bring them inside the top room. While they jump in, drop to the stairs and you'll be safe while you use health, or hit them on the legs - keep using the UV torch and wait to recharge it once it's fully used

If they back off just chase them outside and lure them back in again, keeping your torch light on helps to attract them more

As an addition to this, while you're backed into the stairs they won't be able to "see" you, so you'll earn agility by "escaping" from the volatiles, by running around and attracting them I earned lots of agility, meaning that I got from level 8 to mid-way through level 10 just by moving and "escaping"

I'll edit this and put a map & captures up as soon as I can...

If like me you are too scared to go out at night and probably not actually best suited for this type of game. Progressing the normal story mode I came across an easy point to get this.

Here is a video guide with English commentary for the "Mouths Wide Open" achievement!