fight down vs struggle

fight down is not a noun while struggle is a noun.

Word	Noun	Adjective	Verb	Adverb
fight down	No	No	Yes	No
struggle	Yes	No	Yes	No

As verbs, struggle is a hypernym of fight down; that is, struggle is a word with a broader meaning than fight down:

Other hypernyms of fight down include contend, fight.

fight down (noun)	struggle (noun)
	strenuous effort
	an energetic attempt to achieve something
	an open clash between two opposing groups (or individuals)

fight down (verb)	struggle (verb)
fight against or resist strongly	be engaged in a fight; carry on a fight
	to exert strenuous effort against opposition
	climb awkwardly, as if by scrambling
	make a strenuous or labored effort