Contrary to the other answer and the assumptions in your question: Hard determinism does not, in any way, mean that trying to better yourself does not work. Rather, under hard determinism, whether you decide to "try" to better yourself is also determined. You had no "free will" to decide whether or not to post this question. And you're "destined" to be convinced by this philosophical argument (or not to be convinced).
That does not mean that trying to better yourself will fail, instead it was already destined to be that you would try. It was also destined whether it would be a successful attempt or not.
Similarly, hard determinism does not state that people cannot be convinced to better themselves (or be affected by law, by culture, etc). Instead it means that you, for example, are predetermined to try and convince someone to better themselves (Just like I'm writing this answer); and whether it will work or not is also already determined.
So... back to the question:
Why should we try to better ourselves in a deterministic world?
We should try (or don't try) for the same reasons as you would under a non-deterministic world. The premise of the question is flawed. The truth value of determinism does not change anything.
If you think that people should try to better themselves in a non-deterministic world for whatever reasons, then the same reasons would apply to the deterministic world. If you don't think people should try in a non-deterministic world for whatever reasons, then the same arguments would apply in a deterministic world.