negatives + must do?

I’ve been trying to wrap my head around ~なきゃ/~なくちゃ (and the long forms ~なければ/~なくては) and for the most part it’s okay if I just remember even though it’s negative, it means you need to do whatever the other attached verb is saying. So 帰らなくちゃ means “I have to go home” etc, so that’s fine. But then I have

「元気になるためには、もっと食べなきゃだめだよ」

And this whole ~なきゃだめだ thing is throwing me off. I’m not sure if it means you should eat more or shouldn’t eat more? I actually asked my tutor before, but I’m terribly unorganized and if I even remembered to write the answer down, I can’t find it, and can’t figure out if I already corrected the sentence translation or haven’t yet so I’m still kind of confused.

It kind of sounds like “having to eat more is bad” but I have a vague impression that is actually a trap and it actually does mean “You need to eat more” and the double-negative is just emphasis. Help?