This achievement can be done on multiple levels, although it is recommended to try on "Dead City", where there are 3+ hotspots.
A hotspot can be identified by a beeping noise on your watch which has a built-in Geiger counter. The first one can be found after going into the first building after you gain access to the outdoors. Upon entering the building, you can jump onto the ATM and then jump through the broken glass into a small room with a dead soldier and a red safe key. This room is a radiation hotspot, and you will begin to take damage upon entering it. To stay alive you will need to space out 3-4+ medkits about 15 seconds apart, and continuously change your gas mask filters. After 60 seconds, you will unlock the achievement.
There are also another two areas near a car that is parked near the playground, and inside of an upstairs room where you can find a bolt gun, which can be viewed in the video.