I did this on mission 14 on Practice Mode on Normal Difficulty. Playing on Easy is allowed, and would give you a bit more leeway.
A few things to make note of that aren't in the video.
I started by building that bottom squiggle out of greens, then upgrading them to reds as I had the resources.
When the extra path pops up (with the loops), I blocked the road to make them walk up there. I also upgraded these to reds.
As I gained resources, I built that back line of red infernos.
Around wave 20, I built the 4 infernos in the loop square.
During wave 24, I used Cai's Orbital Laser to weaken both of the enemy dropships so the guys inside would come out weaker.
And there you have it, the achievement should unlock on the score screen.