An over-achiever is someone who works extremely hard to succeed, and then feels low, restless or angry if they do not hit every high mark they set for themselves. It is not simply “a person who does well.” Many people do well and can still sleep at night. The extra meaning here is the push that never quite stops, and the unhappiness when the result is not perfect. Schools use it about students; offices use it about staff who cannot leave a task alone. It can sound like praise — so driven, so strong — though actually it often carries a little worry, as if the person does not know how to rest. You will also see it written as one word, overachiever, especially in American English; the meaning does not change.