Really you can do this anytime, provided you are strong enough to pick up the globe.
However, an easy way to do this is wait until you have eliminated the final Volk gang boss. The remaining Volk scum will rally in one spot, like a city square area, of the Volk territory. Before going to fight them, go grab the Observatory globe. You should be able to kick it off its stand and pick it up. (Note: 3 or 4 star Strength rating may be required)
Carry it to the Volk city square, there should be plenty of Volk there. Just keep throwing the ball and when you have killed 15 gang members, it will unlock.
Note you do not have to kill the gang members in a certain time limit or sequentially. Just any 15 over any period of time.