General:
* Cacklingly: This is the most direct option, formed by adding "-ly" to the noun. It simply means "in a way that involves cackling."
* Loudly: This emphasizes the volume of the cackling.
* Hysterically: This suggests a loud, uncontrolled cackling.
* Joyously: This implies a happy and cheerful cackle.
* Wickedly: This suggests a cackle that is malicious or evil.
More specific:
* Haughtily: A cackle that suggests arrogance or disdain.
* Derisively: A cackle that mocks or makes fun of something.
* Triumphantly: A cackle that expresses victory or satisfaction.
* Frighteningly: A cackle that sounds menacing or scary.
Examples:
* The witch cackled loudly as she brewed her potion.
* The children cackled hysterically at the clown's jokes.
* The old man cackled wickedly as he plotted his revenge.
* The hen cackled joyously as she laid her egg.
Ultimately, the best adverb to use will depend on the context and the specific emotion you want to convey.