I think 'batch' was a typo...
If you beat one of 3DS Pedia's Gym Leaders, who are real people (just in case you didn't know) and who you battle online over wi-fi, you get a
badge under your Username. There are 6 Gym Leaders.
Each gym has it's own set of rules, but they're mostly quite similar and all take aspects from Smogon's OU Tier, so I suggest you take a look at those. They might seem a bit complicated, but they're there to keep matches fair and you need to follow them.
All you need to do to challenge a Gym Leader is to post on their Gym Thread, transfer 3 Play Coins to them, add their FC, get them to add yours, then do an online battle with your team of 6 (they can either be in the Battle Box or in your Party): if you win, you get a badge, if you don't, you challenge them again after 24 hours and pay another 3 Play Coins.
You repeat the process for the other 5 Gyms and you try to get 6 Badges. After that, there is supposed to be a tournament held every 2 months to decide the 3DS Pedia Champion, in which only people who have all 6 badges can participate... But there hasn't been one yet because not many people have all the badges.
If you're going to go for the 6 Badges, then good luck!
(Sorry if what I said was also complicated...)