There is indeed a world record for that.
The record he was going after is owned by Loris Giuliano, who popped 77 balloons in a single minute. (He also could have gone after Ashrita Furman's record of 46 in 30 seconds.) Those are the records listed by Guinness, but David Rush had an attempt in June that claims to have broken both records, including popping 95 balloons in 60 seconds.
That's all interesting, but it doesn't really matter. DiCarlo wasn't even close to hitting the old 30-second mark over the full 60 seconds.
It sounds easy enough, but seeing Rush do the deed makes you realize it's a team effort and requires more skill than you'd guess. That's especially clear when DiCarlo's attempt goes off the rails. His team was not up to par. One of his partners handles balloons like he's got a latex phobia. It even appears that someone off-camera lets him know it was his fault. He looks to someone off-screen and says, "You blame me, though?"