Well... if you are referring to a past tense event wherein a person beat the old world record, then you say that they "set a new world record."

To use the term "set up" in English means to arrange or organize something. But, once again, English is "lots of fun" because you can "set up" a plot in a movie; you can "set up" machinery to be used; you can "set up" balls on a billiard table; you can "set up" someone to be tricked or fooled. In your example it looks like "set a new world record" (beat the existing record world record) is correct. If one were to "set up" a new world record it means organizing what needs to be done to accomplish the task.