topsy-turvily vs head over heels

topsy-turvily and head over heels both are adverbs.

Word	Noun	Adjective	Verb	Adverb
topsy-turvily	No	No	No	Yes
head over heels	No	No	No	Yes

As adverbs, topsy-turvily and head over heels are synonyms defined as:

Other synonyms of topsy-turvily include heels over head, in great confusion, topsy-turvy.

topsy-turvily (adverb)	head over heels (adverb)
in disorderly haste	in disorderly haste