custody battle vs litigation

custody battle and litigation both are nouns.

Word	Noun	Adjective	Verb	Adverb
custody battle	Yes	No	No	No
litigation	Yes	No	No	No

As nouns, litigation is a hypernym of custody battle; that is, litigation is a word with a broader meaning than custody battle:

custody battle: litigation to settle custody of the children of a divorced couple
litigation: a legal proceeding in a court; a judicial contest to determine and enforce legal rights

Other hypernyms of custody battle include judicial proceeding.

custody battle (noun)	litigation (noun)
litigation to settle custody of the children of a divorced couple	a legal proceeding in a court; a judicial contest to determine and enforce legal rights