You actually don't have to complete all of the three tower defense maps troughout the story, you get the achieve by playing three tower defense maps no matter if you done one of them with another character already.
I'm telling you this because the third story td map can give you a lot of trouble. From the second till fourth wave there are mobs incoming which spawn hellhounds and sometimes they spawn them outside the map where you cant kill them (I tried different characters and skills but it won't work to even hit them) and you have to reset the map. Because of this "glitch" (which also occured in deathtrap) I wasn't able to beat this map yet and wasted a lot of time trying. So what I did was create another character and played the first td map again in order to unlock the achieve.
You can of course beat the third map normally, maybe i got really unlucky but it isn't relevant storywise so you can just skip it and get the achieve this way.