Adverb of Degree (meaning "very much"):
* I badly want to go to the beach.
* She badly needed a vacation after that stressful project.
* He was badly injured in the car accident.
Adverb of Manner (meaning "in a poor or unpleasant way"):
* He played the piano badly.
* The food was cooked badly.
* The team performed badly in the game.
As part of an idiom:
* I badly need a cup of coffee. (meaning "really need")
* I badly wanted to tell him off. (meaning "felt a strong urge")
Note: "Badly" is often used in informal English. In formal writing, you might choose a more specific synonym to express the same meaning. For example, instead of "He played the piano badly," you could say "He played the piano poorly" or "He played the piano ineptly."