*SPOILER* For the hard campaign, I finally managed to beat it with a Glass Cannon approach. Final setup was three Radio Plasmoids (+damage upgrades, +health in the later levels) in the front, and two Damage Buffers (+damage upgrades) in the back.
To start, get all three Plasmoids, putting them in the back and top, and two of the cheapest guns for the front and bottom. Only upgrade +health on the cheap guns; they are just there to soak damage until you can afford the Buffers.
Hope this helps; I'm sure there are better setups, but the best defense is a good offense!