This achievement unlocks by experiencing a special disaster in Cities: Skylines after downloading the Natural Disasters DLC. There is only one special disaster in the game; it's called a Chirpnado. It is essentially a blue tornado with blue birds (similar to the Chirper from the game) flying around it. I've provided a video of what a chirpnado looks like; credit should be given for the video to ATV9000 from Youtube.
I wrote this guide to provide some facts and tips on the process of obtaining this achievement.
Firstly, all disasters in the game can be summoned manually - except the special disaster. This means that the special disaster must occur on its own by playing the game normally over the course of time.
Secondly, and to also repel some misinformation that's out there, disasters are completely random and occur completely randomly. (This obviously also includes the chirpnado/special disaster.) In other words, when and where the special disaster occurs is not set in stone. You do NOT have to continue progressing in years on your map for the special disaster to occur. You can simply load a map, let it run, quit once your city has been essentially destroyed by disasters and reload your map. The same disasters will NOT occur again. I can confirm this as this is how I unlocked the achievement. If, by chance, the same natural disaster does occur, it is probably just a coincidence.
Thirdly, it should be stated that this achievement is a luck based achievement, and, therefore, can take anywhere from a few minutes (highly unlikely) to hundreds of hours (more likely). The chirpnado has a very low probability of spawning, somewhere around 0.33%. That technically means that every 303 disasters, a special disaster should occur. This obviously may not hold true in the long run, however. Also, there isn't any set basis of time on how often a disaster will occur. From my experience, you may experience two disasters within 5-10 minutes, and then not experience another one for over an hour.
Fourthly, almost everytime a natural disaster occurs within your play area, your in-game speed is reduced back to the slowest setting. That means, on top of what was said above, if you plan on fully idling this achievement, it will take three times longer. The best and most efficient way to go about doing this achievement is to semi-idle, whereby whenever a natural disaster occurs you turn the speed back up to 3X. You could probably do this while spending most of your time doing something else, like playing on your xbox 360, pc or doing chores, etc.
--- THE PLAN: ----------
So, the plan then is to create a city that does not occupy a lot of space, and a play area that mostly consists of undeveloped land. This is so that you can run the map for as long as possible without disasters affecting your city and eventually destroying it as well as your income. You want as much undeveloped space spread as far away from your city as possible to increase the odds of the disasters occurring somewhere other than your city for as long as possible.
You can accomplish this several ways. A good way to do this is to try to grow your population as much as possible while remaining in the the first map tile you are given for as long as possible, unlocking as many milestones as possible. A good milestone to try to reach is the 30K one; if you unlock this you will have received five additional unlockable map tiles. If you are having trouble doing this, take a look at the Trueachievements walkthrough of the game, where you are guided through doing this.
Once you have unlocked as many milestones as you can with your city in as small a space as possible, start to purchase map tiles in a direction as far outwards from your city as possible. Make sure to use up all of your map tiles so that there is as much available undeveloped land space as possible.
Now go into the game's menu, go to options and turn on 'Use Random Disasters'; slide the frequency to maximum.
Now, it's time to wait.
--- MY EXPERIENCE AND STATISTICS: ----------
Overall, it took me a little over one month of idling and semi-idling to unlock this achievement. For the majority of that time, I was leaving on my console for about twenty hours a day, resting it for about four hours. Even with this, it still took a little over a month to experience a special disaster.
TIME PLAYED BEFORE GRIND STARTED : approximately 260 Hours
TIME PLAYED WHEN GRIND ENDED: 701 Hours
TOTAL TIME OF GRIND: approximately 441 Hours--- OPINION: ----------
This is a brutally time-consuming achievement. It took me over four hundred hours of grinding to unlock it, and that number could have well been much higher than that. This achievement is the worst kind of achievement, in my opinion - luck based achievements. I really don't think it makes sense to go for this one unless it's one of your last achievements in the game, or you are a serious completionist. Regardless, if you decide to stay in for the long haul, you need to be determined or you're probably going to give up early, especially with all the other games you could be playing instead of grinding this one.
If you have any questions or can provide any additional information, please leave a comment. Also, please leave a comment before voting negatively so that I can make any improvements or corrections.