This challenge is pretty tough. At first, I tried a Chariot rush and managed to capture, lose, recapture, and hold an AI's only source of metals, but eventually that AI got another source in trade from one of the other AIs for a Clam Resource. I had a couple of Axemen, but I lost my army of Chariots and it was already pretty late in the game.
I tried again with an Ivory start and managed to squeeze in 4 tightly-pressed Cities. I traded for many techs, had a decently-looking start, but kept having 1 City's production repeatedly sabotaged. No matter, I just had to wait for War Elephants. Hmmm, except that once Monarchy got learned, one AI decided to declare war on me and then a series of chain bribes had me fighting 4 AIs. 4 declarations of war all in a row! With 3 Warriors to my name (it should have been 4 or 5 Warriors, except for my Hammers being Sabotaged repeatedly), and with my opponents being adjacent to my Cities' Cultural Borders, it was immediately game over.
It's definitely going to take some luck (and maybe better opponent choices) to get through to the stage where one can pump out War Elephants.