It's looking like I've made this game not very easy to understand, which is a major problem. In fact, I'm going to have to take a long look at how I implement these systems before I do any more work on this game. I might even scrap it altogether if I can't get it to make sense. For now, though, I made a video with two different playthroughs. Each one shows a different way you can win the encounter and the a few different achievements that are unlockable. Hopefully that helps it all make some sense!
Thanks again for all the feedback, everyone. It's been extremely valuable.