naughtily vs badly

naughtily and badly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
naughtily	No	No	No	Yes
badly	No	No	No	Yes

As adverbs, naughtily and badly are synonyms defined as:

Other synonyms of naughtily include mischievously.

naughtily (adverb)	badly (adverb)
in a disobedient or naughty way	(`ill' is often used as a combining form) in a poor or improper or unsatisfactory manner; not well
	to a severe or serious degree
	very much; strongly
	with great intensity (`bad' is a nonstandard variant for `badly')
	in a disobedient or naughty way
	evilly or wickedly
	unfavorably or with disapproval
	with unusual distress or resentment or regret or emotional display
	in a disadvantageous way; to someone's disadvantage
	without skill or in a displeasing manner