What part of speech is greedily?

Greedily is an 'Adverb.

Remember in English, Words ending(suffixed) in '-ly' are adverbs.

Words ending in '-al' are abstract adjectives.

A common mistake is the use of the Word 'sisterly'. e.g. my 'sisterly sibling' is incorrect. 'Sibling' is a noun and is conditioned by an adjective. So the statement should read my 'sosorial sibling'. Note the spelling. 'Sosorial is the adjective.