performance vs achievement

performance and achievement both are nouns.

Word	Noun	Adjective	Verb	Adverb
performance	Yes	No	No	No
achievement	Yes	No	No	No

As nouns, achievement is a hypernym of performance; that is, achievement is a word with a broader meaning than performance:

Other hypernyms of performance include accomplishment.

performance (noun)	achievement (noun)
the act of performing; of doing something successfully; using knowledge as distinguished from merely possessing it	the action of accomplishing something
the act of presenting a play or a piece of music or other entertainment
any recognized accomplishment
a dramatic or musical entertainment
process or manner of functioning or operating