Attached is an example of how to win every scenario (bar Triple Repulse which is broken under the latest patch, once this is fixed I'll update).
Every one of these are my *first* win on a scenario, the first way I figured out how to beat it. This means that they're likely not the best way, nor the cleanest, nor the highest in terms of points, but nor are they carefully honed to make me look great while I beat the scenario in a way you were never going to figure out without fifty attempts and a few wins under the belt.
Under the latest MA patch (204) I have endless problems viewing some of these replays. I believe this is a problem with the patch affecting the scenario, rather than the replays themselves. If you have issues watching them under 191, let me know and I'll just have to re-record them all when the next patch comes out.
Losing to the AI?
HOWTO: Beat the AI
Losing online?
Quitch's Replays thread