This will require a bit of a grind but fortunately, like many Tropico achievements, it can be unlocked in sandbox mode. Start up a new game in Modern Times with unlimited money, and the difficulty turned down if you like.
Quick build a couple solar plants, a few research labs, and the space program. Upgrade everything, max the budgets, and hire foreign workers to fill all slots. Once you have 5,000 Knowledge points saved up, go to the space program and launch a prestige mission. It says it takes one year but on max budget and staff it should only take 240 days.
Once the mission is complete, there is a chance to get a special event. You’ll know it you get it because Penultimo will say something and you’ll get the achievement. Keep running space program prestige missions while quick building whatever you need to keep people happy. Every prestige mission increases approval by 5, so that will help.
It took me about 25 in-game years to finally get the special event, but part of that time was spent setting everything up and I didn’t always start the next mission as quickly as I could have. Just keep those Knowledge points rolling in so you can fire off a new mission every 8 months and you’ll get this eventually. I got it after about 15 missions.