I’ll try a different theory now, before I attempt research.
Let’s consider the possibility that the phrase is an ignorant permutation of “somewhat fiercely.”
We can readily find analogs for both components in familiar speech. There’s the expression “somewhat of a,” which is an ungrammatical substitute for “something of a”:
— He’s somewhat of a dandy. (s/b “He’s something of a dandy.”)
— It was somewhat of a downer. (s/b “It was something of a downer.”)
Omitting the -ly or using the adjective in place of the adverb is common in uneducated speech and also in careless or casual speech generally:
— We fixed it up real good. (s/b “really well”)
— You have to speak really quiet. (s/b “quietly”)
— He was looking at me very weird. (s/b “weirdly”)
It’s not hard to imagine speaking of doing something “really fierce.” If I can entertain that, I can also imagine “somewhat fierce.”
The problem with this is that “somewhat” means “moderately,” and “something fierce” isn’t moderate. It’s extreme. But the phrase could have evolved over time.
It’s still adverbial in any case.