Defense Grid 2

I did this in Normal Story, but this can be done on any mode/difficulty so I'd recommend Practice on Easy. (Credit to Clowny for testing)

Also, you CAN build boost towers. I didn't when writing the solution, but did when I originally unlocked the achievement. (I earned the achievement on accident surprisingly enough.)

Anyway, I did this on mission 16 (on Normal Story as said above.)
Right next to the orange core housing, there is a platform that has 3 intersecting squares (made of 10 tower spots.)
What I did was put 5 cannon towers along the edge of this to hold off most of the early waves.
After wave 3 I made them all level 2.
Some enemies made it past this group of towers during wave 5, so I filled the 3 sets of 2 squares next to the blue housing (I didn't have enough for all 6, so I filled 4 and then waited until I had enough for the other 2.)
During wave 15 I had trouble with the healers since my cannons had the temporal upgrade, so I upgraded all the ones at the blue core housing from level 1 to level 3.
During wave 24 I upgraded the 5 on the left to level 3.
During wave 26 some racers almost got away from me - the temporal upgrade probably saved me here. You don't HAVE to save all the cores, but if you want to, you might need to build a few more towers for this wave than I did. Rewind is your friend.
I was able to make it through the rest of the level without any problems. You'll have PLENTY of resources if you want to build more things, maybe build a bunch of extra cannons if you need the 100 achievement.

At the score screen the achievement should unlock.

I did this achievement on level 12. My tactic was to make the aliens go the long way round on the bottom part of the map by blocking of the short bend and also blocking the 2 middle squares, I then blocked off 3 of the 4 passages and only left the one closest to the cores so they have to snake round. At this point I started building cannons on the big pillar opposite the core and upgrading them all to level 3. If you keep upgrading all of your towers to level 3 you should have enough fire power to get you through the level but to be safe keep adding cannons to the start of your snake path when ever you get spare resources.

If you would like a visual guide to what I have just explained I have included a video below on how I got this achievement .