Only seen in one noncanon (to the main timeline, at least) entry, Circle of the Moon, the Hunter Whip is the chosen weapon of Morris Baldwin (at first) before he passed it along to Nathan Graves some time before the events of the game. While it begins as a simple leather whip, over time and the collection of DSS cards, it becomes the single most versatile and powerful weapon in Castlevania, able to take on dozens of forms, from wreathing itself in cosmic elements like flames, ice, or the void itself, changing into swords, axes, and spears (even an absurdly powerful handgun!), becoming full bodied summoned creatures that appear briefly yet powerfully, and even changing Nathan himself into a skeleton or a... teddy bear... thing!
The power of the Hunter Whip is almost as varied as the user's imagination, and if we understand the DSS cards to simply be a gameplay metaphor for Nathan's growing mastery of the whip (especially as they are not once mentioned in dialog), imagination and focus may in fact be the only limit this weapon rightfully has. Whatever similarities the the Vampire Killer of legend the Hunter Whip may initially possess, it is clearly in a class all of its own by the time it is fully mastered, having surpassed the Vampire Killer's potential for sheer destruction long before.
I have some thoughts as to what the whip is, and indeed its origin.
While there is nothing spoken in game about the specific nature of the Hunter Whip, its basic traits seem to align well with the Whip of Alchemy wielded by Leon Belmont in 1094, especially as that whip was able to change its elemental nature as well with some swappable applied phlebotinum before becoming the Vampire Killer. In addition (and I fully admit this is reaching at straws) Trevor Belmont's gameplay mode in Curse of Darkness (combined with gameplay elements from Juste Belmont in Harmony of Dissonance) imply that it is still capable of doing this depending on specialized tips added to the weapon. If anything, the greatest difference is that the Hunter Whip changes to greater degrees and does so without any add-on parts.
This leads me to believe that the Hunter Whip was created as a perfection of Rinaldo Gandolfi's original research, perhaps by him directly, or simply a gifted Alchemist picking up after him. It's clearly everything Gandolfi could have wished his own weapon to be originally. This does assume heavily that Lament of Innocence (or a version of those events at any rate) occurred within Circle of the Moon's timeline as well, but in my mind it seems to fit: that the Hunter Whip is an offshoot/refinement/perfection of the research that created the original Whip of Alchemy, a sort of cousin to the Vampire Killer that while exceedingly difficult to master can be wielded by anyone (or almost anyone) without the need for a Lecardeian Unlocking Ritual. The sheer potential of the weapon remains mind-boggling, and Dracula and his ilk might be better off staying dead if someone with a firm mastery of the Hunter Whip is keeping watch.
It's a shame we didn't see more of it, but then again, the single vague appearance and description is what made this theory possible in the first place so... silver linings.