Okay, I have the 1,000 tag badges in both my NA and Japanese copies, over 900 of them earned myself. One, you need 2 copies as well, and you do NOT have to clear out the StreetPass plaza on the 3DS, but you DO have to clear out the HHS plaza to get the tags. So, turn them on, put them in sleep mode, get the green light, start the game, go to the plaza- get the item if you wish, they're random, then you've gotten the tag. However, with just 2 systems, it will take you over a year of daily tags, because in theory you can get 3 a day, but in reality, you're only going to manage 2, because it literally HAS to be AT LEAST 8 hours, meaning they have to tag to the 8th hour by the second, meaning it'll take 24 hours, 3 seconds to get 3, so you can only mathematically get 2.5 in a 24 hour period on average because of the minimum. You can see how after a year, that's only 730 tags.
You really need 3 systems, because you can do what I did, play musical systems where you tag 2 of them, then switch. For example I'll use the 3 variants to make it easy. Put one copy into the XL, and the other into the 2DS. Tag them. Make sure to go to the HHS plaza and empty it out, otherwise the game may not recognize those tags! Then take out the XL one, put it in the 3DS one, tag the 2DS and 3DS. Then, take out the 2DS one, put it into the 3DS, and tag the 3DS and the XL. Eight hours later, repeat. That'll give you 6 tags a day! Yes, you need 3 systems, and 2 games and play musical systems constantly switching. It'll also drastically lower your average playtime, because you're only "playing" for like a minute to get the HHS cleared out.