Living Towers consist of 3 different towers; Hourly, Daily and Premier (Weekly). Each has a different number of Kombatants that you will face under varying circumstances. It's an attempt at a timed challenge mode that offers a score based on your performance and offers global rankings for the challenges.
As of 4/14/2015 you can repeat the same Living Tower multiple times in order to earn progress towards this trophy. This saves you the effort of having to constantly keep checking for new challenges to do.
EDIT: It seems that the hourly challenges are consistently 5 matches long and have one extra condition tied to them. That said, it would be quickest to keep completing these challenges and passing up on the daily/premier challenges. Even after the latest patch, repeating the same tower seems to work as well.
Another thing worth noting is that you will earn a unique Kostom Kombat Modifier upon completion of each unique hourly tower you complete. If you're unsure of whether or not you have completed a tower, simply look to see if you have a personal best/ranking on the lower-left portion of the screen. For this reason, it would be wise not to simply play the same towers repeatedly in order to knock this out quickly. (Thanks Markyshizzle for the reminder!)