Very simple method to beat this level - sure fire way to win. Here's the jist of it:
1. Start with your original 1 block.
2. Build 3 blocks out, front and back.
3. Build 2 blocks down in the very front, but only 1 block down in the very back.
4. Drop your machine to the ground floor.
5. Build 6 blocks on top of the machine.
6. Put a cannon on top.
7. Start the mission, let the machine tilt back, and shoot.
Easy win, no armor required.