What are Special Miis?
Solution 1:
Special Miis are Miis created for official promotions. Some are official game character Miis. For example, Capcom created Resident Evil: Revelations for Jill, Chris, Parker, and Jessica. Others, the kind StreetPass Mii Plaza gives achievements for, are gotten by StreetPassing special demo kiosks or Nintendo employees.
Special Miis are identifiable via their golden pants. You can't share QR codes for them, and apparently you cannot send them directly to someone else without losing them from your own plaza.
If you're trying to get that achievement, your best bet is to go to events like Gamescom, Tokyo Game Show, or PAX.
Nintendo also sent an Iwata Mii out via SpotPass on March 25th in Europe, and a Reggie Mii on March 27th in North America, to celebrate the first anniversary of the 3DS's release. You can meet them at StreetPass Mii Plaza and trigger the achievement.
(Special Miis are not new to the 3DS; the Wii also had them, but they were much less used given the poor state of WiiConnect24 outside of Japan.)
Solution 2:
I was able to find a couple golden pants Miis through the internet and scan their QR code, but I have never Streetpassed with any (and I don't think it counts that way). Its because some of them were given out as QR codes in magazine ads and the like. These are Japanese ones from what I've found. They also seem to have a lot of special Miis for various celebrities.
Hopefully they will give some out via the internet. I heard people randomly received an official Nikki (from Swap Note) though I don't think she was a gold pants one. She did not show up for me though. It may have been because I already scanned the Japanese version.