Okay so all the other dragon slayers have an obvious element to their magic. Even with Acnologia's roar on Tenrou Island, there was no direct element to his magic. The only thing I could think of is just that his name is "The dragon of the apocolypse". So do we know what it is yet or not?
The dragons we have seen so far do follow a unique theme and magic which is not necessary an "element". This table on the wiki sums it up pretty nicely. Acnologia is known as "The Black Dragon". (There is also a white dragon, Weisslogia). So the theme of Acnologia is "Black". What exactly are the limitations of its "black" magic are haven't been shown in the anime/manga.
However, there is a reason why Acnologia is "different" from other dragons.
Acnologia is a cataclysmically powerful Dragon Slayer that can take the form of a Dragon.
Born over 400 years ago, Acnologia was one of the first Dragon Slayers to come into being, entering the Dragon Civil War on the side supporting coexistence. Acnologia and a group of other Dragon Slayers, however, disregarded the cause their comrades fought for, and killed every Dragon they could, bathing in their blood. Due to the overuse of his Magic, Acnologia's physique eventually turned into that of a Dragon's, and he proclaimed himself to be the Dragon King. This event was forever etched into history as the Dragon King Festival.
You can read more about Acnologia's history and the Dragon King Festival on the wiki (it has a decent summary) or read the manga. This is discussed in Chapter 301 of Manga.
Acnologia's element is etherious. Which is the combination of all other elements of magic. He can eat up any magic.
There is a theory that has a great explanation on what it might be. It is said in this theory that Acnologia is the Etherion Dragon Slayer. Basically Etherion also known as Ethernano is the mix of multiple different elements. You remember when natsu ate the part of the lacrima? Well, that was Ethernano. (Honestly the video below explains it 10x better than I can).
Here is a like to the YouTube video: https://www.youtube.com/watch?v=exDA3rQF9Zk