The skull of Achelousaurus possesses three dense bone groupings along the nasal, some of the frontal, and the supraorbital ridge. The nasal ridge is always depicted as a shield like protuberance or a straight up jutting protuberance of horn, but given the evolutionary trends of the Centrosaurine family, specifically the reduction of brow horns while a tall nasal horn was becoming prominent and then reduction of the height and an exaggeration of the forward sloping of the nasal horn, most prominent in Einiosaurus, this nasal boss could be then, in part, a horn core for a nasal horn that is in the last vestiges of the forward facing prominence found in Einiosaurus, especially because of the perceived close relationship of Einiosaurus and Achelousaurus. It is rarely shown as such, but I think that the end of the nasal bone structures may have supported at least a tiny horn which jutted straight forward off of the nasal bone, almost like a digging horn or the adornments found on male narwhals rather than just a dense patch of bone.
Most depictions of Achelousaurus show that nasal ridge as a boss of dense bone, which may indeed be correct and is obviously the most popular interpretation. The eye-brow ridge, or suprorbital ridge, bone is certainly dense and unless the alternate theory of Pachyrhinosaurus horns jutting from dense bone material is applied, then the dense ridges of bone are merely a shield like covering over the eyes much like we would find in the extremely thick domes of Pachycephalosaurs which leads to one solid theory for these ridges: Centrosaurines, once the evolutionary trend of horn reduction had been taken this far in later Centrosaurines that they possessed only thick areas of bone where horns once were, had changed from piercing defensive weapons/rival intimidators to headbutters like modern goats, though obviously much larger. We would then probably expect to see more of an ability in the hips to rear, like goats, or more power at the very least to sprint into a rival or predator, meaning that the cow-like structure of the body may need to be altered a bit.
One thing that certainly did not change, in terms of evolutionary trends (I put together a presentation for a posters and presentation class I am taking for my MS on Centrosaurine evolutionary trends, so I apologize for the heavy use of that phrase this week!) is that the parietosquamosal frill is still quite well adorned. The peak of Centrosaurine frill design, arguably, is the ostentatious frill which is exemplified by Styracosaurus with its lightweight protection and multiple spikes all along the ridge of the frill. Achelousaurus has a much simpler frill design, but it is still considered an adorned frill. The two spikes at the apex of the frill are standard for all Centrosaurines save a few (Centrosaurus, Coronosaurus, which used to be a Centrosaurus species until recently). Frills of the Centrosaurines are truly works of art. This is a little more minimalist in its approach than other Centrosaurines, but it is still a wonderful looking animal.