topsy-turvy vs heels over head

topsy-turvy is an adjective but heels over head is not an adjective.

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

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

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

topsy-turvy (adjective)	heels over head (adjective)
in utter disorder

topsy-turvy (adverb)	heels over head (adverb)
in disorderly haste	in disorderly haste
in a disordered manner