I'd recommend changing the name of the stat "skill." That could get confusing around the table, since at least a non-zero number of players will refer to stats as "skills" too.

Making Beasthood and Insight opposed stats is a beautiful touch.

Making essentially all combat checks opposed rolls is a really interesting mechanic that I'd love to see expanded on. Stamina Points also work really well with this system. I would recommend that parrying and dodging also require SP. Players then have to make an interesting decision: do they use all of their points on their turn, or do they leave one or two SP in reserve to defend themselves before control returns to them and their SP regenerates. That is also pretty similar to how From Soft's games handle stamina, albeit in real time.

I'd personally give stealth a little more crunch. I like what you have with the different types of being noticed by monsters. 

Unless I missed it, what happens upon player character death?

This is really shaping up well, and you could easily make a non-Bloodbourne version of this game into something standalone. I'm excited to see the next draft.