Once you take over a city you'll be able to send characters to the fighting pits to complete missions against Enemy Captains.
Go to your "Army" screen. Find a couple of captains you don't care if one gets killed. Select one with
to issue a command, then hover over the second and hit
to send them to the fighting pitt. Go to the fighting pitt and watch. After one dies, the achievement will unlock.
NOTE: if you have any other pitt missions open. You'll have to complete that first.