badly has 9 distinct synonyms spread across 7 of its 10 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is well.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
without skill or in a displeasing manner
“she writes badly”
in a disadvantageous way; to someone's disadvantage
“the venture turned out badly for the investors”
with unusual distress or resentment or regret or emotional display
“they took their defeat badly”
1 of the 10 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for badly.
Synonyms, antonyms and the broader and narrower relations for badly come from Princeton University’s WordNet. Full sources and licences.