I don't know how many people this applies to, because I've read many times that people just dump one game and it works across all of theirs just fine, sadly, this isn't the case for me and I've seen about 3 people make a thread asking why they're getting this error, and they've gotten no answers basically.
So turns out, if I'm correct, it's because of the manufacturer.
All of my ROMs aside from Smash, didn't work online with my header information from my own dump of Animal Crossing.
And I noticed something, Smash was the only game I had where the manufacturer byte was AE(OKI-Semiconductor), and that's the same manufacturer of Animal Crossing. Everything else gave me error 002-0123.
Mario Kart 7 and Final Fantasy: Curtain Call were the main games I wanted to play online, and those are both C2(Macronix) games.
I have a friend with a 3DS and about 10 games that he doesn't care for, I managed to get him to dump Pokemon Y and a few other games(Which actually leaves me with a header for each manufacturer) and Pokemon Y just so happens to be C2. I applied that header to MK7 and TFF:CC and whaddya know, they work online now. So if all of this is correct, you want at minimum 3 3DS dumps to ensure compatibility of all roms.
Read your dump's header information using Sky Army Knife and see if it is either an AE(OKI Semiconductor), C2(Macronix), or 45(SanDisk) based game, and then check the base template for your game and look at its chip ID so you can tell which header and EEPROM to apply to get that to work.
Remember:
C2 = Macronix
AE = OKI Semiconductor
45 = SanDisk.
My Animal Crossing: New Leaf US dump:
There may be many of you who know this already, but this is mainly for those people who didn't get an answer when they asked last week, because I was one of those people.