To "live authentically" means quite different things to different people, I think. This phrase will likely take some explaining to get across even to many native English speakers, no? From a stereotypical, individualistic American perspective, this may mean sticking to your ideals, even if the people around you challenge you. To a scientist, this might mean always remaining skeptical.
From Naver, I found some example sentences that may convey some meanings similar to what you are looking for with the search query "be true":
- 학생들은 자신에게 충실할 것을 맹세했다. The students swore to be true to themselves.
- 나에게 솔직해져 봐. 속마음을 말해줘. Be true to me. Bare your heart.
- 대부분 그들은 진실하지 않을 것이다. Most of them won't be true.
I too have heard "똑바로 살아라" as mentioned in Jihyung Kang's comment. This points to a more conservative notion of "living properly", or "straight". A statement like this may capture some of the virtues of honesty and diligence that might come with living "authentically". But it also brings with it other connotations (such as suggesting comformity and interacting well with society, which being "authentic" may not, as far as I understand).
In short, many phrases/idioms/etc. contain culture specific notions/information that make direct translation impossible; but if you know more specifically what ideas of an idiom you would like to capture, you can probably get closer to what you are trying to say.