Whatever the highest rank is.

Arch- usually indicates the highest form possible without utter transcendence into a different form, or at least a, well, overarching rank of some sort. (Semantically related, but not etymologically, apparently. At least not directly. But I digress.)

It is, after all, why the name of Arch Linux is what it is (so sayeth Wikipedia). The creator wanted it to be the best with no equal.

An arch-vegan might be one best at not only avoiding animal-based produce but also convincing people to convert to veganism, as well as making normally well-adjusted vegans feel that they're not being a good enough vegan.