Adjectives are words that modify nouns or pronouns by defining, describing, limiting, or qualifying those nouns or pronouns.
Adverbs are words that modify verbs, adjectives, or other adverbs and that express such ideas as time, place, manner, cause, and degree.
Use adjectives as subject complements with linking verbs; use adverbs with action verbs.
Good is an adjective; its use as an adverb is colloquial or nonstandard.
Well may be either an adverb or an adjective. As an adjective, well means "in good health."
Bad is an adjective used after sense verbs such as look, smell, taste, feel, or sound or after linking verbs (is, am, are, was, were, and other forms of be).
Badly is an adverb used after all other verbs.
Real is an adjective meaning "genuine"; its use as an adverb is colloquial or nonstandard.
Really is an adverb.
NOTE: Really has become an overworked adverb; therefore, one should use alternatives such as very or exceedingly whenever possible or leave out the adverb entirely.
Sort of and kind of are often misused in written English by writers who actually mean rather or somewhat.