There's a total of 18 Radio Towers, but you only need to take over 9 for this achievement, which is pretty easy, though you will be unlocking them all as you pay through the game. The Towers are located by the Radio Tower icon on the map. Simply head to one and you'll then need to reach the top by climbing up it. Doing so, you'll be awarded with your map being uncovered and a new gun being free from any store.
There are no enemy AI involved with these, you simply must find your way to the top of 9 for the achievement to unlock.