To a severe or serious degree:
— Fingers so badly frozen they had to be amputated.
— Badly injured.

synonyms: gravely, seriously, severely.

`ill' is often used as a combining form In a poor or improper or unsatisfactory manner; not well:
— The car runs badly.
— He performed badly on the exam.

synonyms: ill, poorly.

Roget 649: badly etc. adj.; wrong, ill; to one's cost; where the shoe pinches.   

Evilly or wickedly.

In a disobedient or naughty way:
— He behaved badly in school.

synonyms: mischievously, naughtily.

With great intensity (`bad' is a nonstandard variant for `badly'):
— The injury hurt badly.
— The buildings were badly shaken.

synonym: bad.

Very much; strongly:
— I wanted it badly enough to work hard for it.
— The cables had sagged badly.
— They were badly in need of help.

synonym: bad.

Without skill or in a displeasing manner.

In a disadvantageous way; to someone's disadvantage:
— The venture turned out badly for the investors.

synonym: disadvantageously.

Unfavorably or with disapproval:
— Thought badly of him for his lack of concern.

synonym: ill.

With unusual distress or resentment or regret or emotional display.