attainment vs ability

attainment and ability both are nouns.

Word	Noun	Adjective	Verb	Adverb
attainment	Yes	No	No	No
ability	Yes	No	No	No

As nouns, ability is a hypernym of attainment; that is, ability is a word with a broader meaning than attainment:

attainment: an ability that has been acquired by training
ability: possession of the qualities (especially mental qualities) required to do something or get something done

Other hypernyms of attainment include power.

attainment (noun)	ability (noun)
the act of achieving an aim	the quality of being able to perform; a quality that permits or facilitates achievement or accomplishment
arrival at a new stage	possession of the qualities (especially mental qualities) required to do something or get something done
an ability that has been acquired by training