Which are achievements of the Han dynasty?

There are many achievements in that time. For instance, the papermaking technology was invented in that time. The textile technology improved a lot, so that the silk was widely used then. The Chinese medical developed fast and many famous Chinese doctors such as Zhang Zhongjing lived that time. In education, the Confuciansim established his status in that time, which had deep effect on Chinese education and culture. These are all I know and hope it can help you.