besides, you made a mistake . the Chinese character 再means again . if you wan to say you are doing sth , you should use 在 . the pronunciation of them are the same , but their meanings are different . hope my explanation is useful to you .

be successful through one's own effort. 也就是说 通过自己的努力、拼搏获得成功。

意思就是，你的事业有所成就！

在某一个领域有所作为

You may be puzzled by the character "混"，actually here it means "to work hard". then "自己的一片天" means metaphorically "carving a niche for yourself"。 now，you get the whole meaning?