An irregular adverb is an adverb that is irregular, i.e. it is not a regular adverb, which in English follow the rule add -ly to make an adjective into an adverb. Various definitions of "irregular adverb" either include or exclude the (b) the semi-regular bare adverbs, where the adjective and adverb share identical forms - note that degree of regularity is a spectrum not a dichotomy. Bare adverbs are discussed in their own article.
Otherwise, there appears to be only one completely irregular adverb in English - "well", which corresponds to the adjective good.