In the sentence, "I am soaking wet", 'I' is the noun, 'am' is the verb, 'wet' is the adjective, and 'soaking' describes the extent of 'wet'. So would 'soaking' be classified as a "helping adjective", so to speak? Or just an adjective? Or is there a better term to describe this?
One can be barely, slightly, moderately, soaking, and dripping wet, all describing a degree of wetness. As the -ly suffixes on the first three in the list suggest, this is the task of adverbs, even if by form, soaking and dripping are present participles without verbal force.
This is hardly an unusual construction: burning/scorching/piping hot, freezing cold, raving/barking mad, but deafeningly loud, exceedingly hungry.