The whole idea of making a monster character feel fresh is tricky, honestly. Everyone's pulling from the same big archetypes—the tragic werewolf, the morally gray vampire, the ancient god learning humanity. I think the trick isn't about avoiding those entirely, but about finding the weird little pressure point that flips them. Instead of a vampire who broods over immortality, what about one who's just profoundly bored and takes up competitive knitting or urban planning to pass the centuries? Their monstrous nature manifests in a compulsive, obsessive need to perfect a sweater pattern, driving them to kidnap yarn store owners. It's the mundane obsession layered over the supernatural power that makes it sing.
Another thing I see writers do really well is borrow physiology from unexpected places. Why stop at wolves and bats? Look at deep-sea creatures, fungi, or even geological processes. A monster whose biology is based on a slime mold, communicating and hunting through chemical trails, creates a completely different set of rules and conflicts than a standard predator. Their 'humanity' might be expressed through the patterns they grow their colonies in, or the colors they secrete when feeling certain emotions. That sort of thing forces you to build the character from the cellular level up, and the uniqueness comes naturally from that foundation.
It's less about designing a cool monster and more about designing a person whose monstrous traits fundamentally alter how they experience the world. The best ones make you forget they're a 'monster character' and just see a character, full stop.