If you achieve something, you've reached a goal. Achievements aren't accidents. If you stumble upon a treasure chest, you haven't achieved something; however, achieving a promotion to become CEO is another story.
If someone asks you to give an example of the word achieve, you can always reach for Shakespeare's much quoted remark from his play Twelfth Night. In Act II, Scene V, the character Malvolio says, ". . . some are born great, some achieve greatness, and some have greatness thrust upon 'em." Pundits like to throw that quote around when talking about politicians. Of course, they usually disagree about if, when, and how the politician achieved greatness.