This is hard. Must say, I don't think that even I, the creator, would complete it to its last city in the given time. But at least, you should give it a try. This is a compilation of the most important (and others not so important) cities in the world. And also, proof that you are a master when it comes to geography and keeping up with profound cultural conversations with your friends. I would try it if I were you.
Note: this test is based on population, GDP and global impact. This last one is to employ more diversity in the test (most Chinese cities have got greater population and GDP than many of the non-Chinese ones, however, only the most impactful on the world will be on the test).