The problem for this map is that (I don't know why the shield nodes aren't showing on the screenshot above), but that big block in the center is protected by a shield node. If you are on challenge mode the turrets have a max range of 5. The thing that was setting me back so much was that screaming node in the center. That screaming node is 6 tiles away from most of the upper and lower paths you could build on. And the ones that are within 5 still means it'd take 50 shots to take it down.
I didn't have enough time remaining for such a strategy the first time I did this. So that was out the window. I went through the last 3 maps on landmark instead of challenge assault. So I could finish stage 4. Now I'm waiting on the 50B PL to start stage 5 :/