After completing the puzzle 'In the Name of the Sphinx,' return to the Sphinx interior later to find a rap battle in the works.
Listen to the rap (or much as you can bear to), then choose the winner. There are no long term ramifications to this choice, save that you'll have to listen to that same rapper one more time at the final showdown.
The next such contest is on the castle roof.
The venue after that, despite the announcer clearly referring to the 'plains' of the Old West, is atop a very high bluff.
Then a Sakaar rooftop overlooking Asgard.
The big finale (though they don't mention the location) is on the very top of Knowhere.
There are four contestants this time- pick the one you like best to unlock the Police Quad vehicle.