You are looking for soap bars with a rope at the end, just like the achievement picture shows.

Note that there are more items than what you need to get the achievement.

Here is a close picture of one :

There are 2 outside sections. One is a large open area while the other is small and has a lot of stuff in your way.

The open area looks like this :

A soap is hanging from the antenna:


Now, from the screenshot above, drop your view and go look in the corner or the map (to your right, still outside) and you'll see another :

In the other section, still outside:

What you see above the Soap is the path to the elevated area where you can weld a door and look at the zone from above. Now from the screenshot, if you look to your right, you'll see a "bridge" between 2 buildings. Move towards it and you'll it on the ground:

The easiest one: Right behind you, at the spawn location, on the other side of the door (Thanks to Speedy223)



From the last picture of the Outdoor section, if you go under the "bridge" you'll see an entrance and you'll find another soap right pass the doors:

Now, I can't make you a path to collect them all one after another because I'm still learning the map but here are the other locations.

As you play you'll find a dining hall /cafeteria and if you look on one side you'll see:

The soap is right above the tray in the picture. Now, step back in the dining hall and you should see another (the tray and service section is bottom right, under the arch in the picture):


From there, if you turn 90 degrees to your left and you'll see a corner that looks like a Zed spawn with a fire, the soap is right there in the middle:


If you happen to go to the lower parts of the map, still inside, you'll end up in the showers or the locker room, which is connected to the showers. There you'll find 2 soaps:

The other is in the first toilet on the left. You can see the wall next to it in the picture above, left of the first pillar.




Then there are the ones spread around:

Those desks are under the stairs, near the broken window from which I took the first screenshot for the open area, outside.


There is one near a shop, right under the "02" you see on the back wall:


Another:
To you left you have cells and there is a steal catwalk you can move on. A Zed spawn is a ladder connected to that catwalk.

I hope it helped but remember you only need to find and destroy 10 out of the 12. Once it's done you will see a message prompt and say you unlocked the achievement Perilous Prison.

Congrats!