Astonishingly is an adverb. The adjective form is astonishing.
As you spelt it in your question, ASTONISHINGLY.
"I gasped for breath at the sight of the astonishingly beautiful painting."
The part of speech for this particular word is a noun.
part of speech
The part of speech for "answer" is a noun.
what part of speech is beneath
adverb
The part of speech for "explicit" is an adjective.
The part of speech for "lecturer" is a noun.
The part of speech for "rapid" is an adjective.
The part of speech of "came" is a verb.
The part of speech for "breezy" is an adjective.