"Bad", as an adverb, has both a standard use and a questionable use, in that the latter can sound incorrect.
Standard use (mostly spoken English):
He didn't do bad in last night's game, actually.
She a bit bad off at the moment, but she gets paid at the end of the month, so.... (AmEng.)
You don't seem to want this bad enough.
When bad is used as a near-synonym of severly, it is often seen as less than standard.
He hated her bad.
She is bad sick, so she can't go to work.
And bad is more common than badly after a copula (linking verb):
I feel bad/?badly.
The food tasted bad/?badly.
And let's not omit the slang sense of "bad", which means "good".