Made a minor edit: It appears to be "Limit Cut", not just "Limit", and some have translated it as bosses (plural), but it could be wrong.

Pure speculation, but I talked with @xenosaga7 on Twitter about this. It's possible this is the equivalent of Org. XIII Data Battles from 2FM. "Limit Cut" is what Japanese fans would call the data fights (occasionally used by people who modded 2FM, so I've seen it before). It wasn't ever used by the developers, but it was common enough the devs may have heard it and latched on. Also, in 358/2 Days, the ultimate attack the players can use, Final Limit, is called "Limit Cut" in Japanese: same Katakana as here (I can't read Japanese, literally just compared the characters lol). Could be a total coincidence, but people were expecting/hoping for this kinda thing anyway.