Is Alchemy supernatural or something of science?

It's up to you as the writer. I would make a science-like magic.

Alchemy is a metaphor for 'inner' transmutation/transformation!
The clueless take it literally and run off seeking 'philosopher's stones' and the 'Universal solvent'...
For those capable of piercing the 'veil', the arcane becomes the mundane...
Nature is ALL inclusive! There is nothing beyond existence, beyond Nature!
There is no 'supernatural' other than in the imagination, and the imagination is perfectly Natural as are the thoughts/images therein!
The 'literalists' went on to do science.
The 'piercers of the veil' went on to become Enlightened!

You could come up with some mad chemistry with chemical formulas and stuff, but if it's a horror story i would make it something more creepy and have some old forgotten spells or something.

Well Alchemy is typically thought of as converting lead into gold (although it is actually much more than that). Scientists have done this before using a nuclear reactor, so I'd say it's something of science.

My suggestion would be to make it something that seems magical, but that can be explained by science.

Look at protons. the sun converts hydrogen into helium and so forth
thats alchemy in science. conversion of matter