Rip, I probably should have known that my lack of playtesting was gonna catch up to me eventually. I did think that Barriers was a hard level, but I didn't think that it would be that hard.
You're supposed to beat it by ignoring the bottom two fountains and only playing defensively at first. Try keeping your tanks near the factory (the factory's repair capabilities really help), then charging in and taking the entire map all at once when you've built up a large enough army. You do have to move your tanks around a bit to avoid enemy shells though.
You can also skip the level if it's still too hard, even with these tips. I forgot to mention this in the tutorial, but the levels are all unlocked at the start, so they can be played in any order. While they're supposed to be in ascending order of difficulty, you may actually find some of the following levels to be easier.