Can be any tower: Living, Hourly, Klassic, Test your Might, Endless, etc.
The fastest way to get though this is to play Endless tower, win a match, then walk away while the CPU defeats you. This technically counts as completing a tower.
BONUS! 10 Living towers gets you Dark Empress Kitana
BONUS! Winning 15 matches in a single Endless Tower run on endless tower wins you Kahnum Mileena