People will die to hunger, when you don't have any supplies left. Make sure you're travelling fast and always have some renown to get yourself some supplies, especially when travelling with Rook's caravan.
Make use of this guide to see the outcomes of random events: http://hubpages.com/games-hobbies/The-Banner-Saga-Walkthroug...
make sure you choose options giving you supplies and not increasing your day count.
At the start of chapter 4, you'll need supplies for around 12-14 days to make it to Wyrmtoe, and they coast a lot where you start, make sure you've enough renown, otherwise you've to hope for some really good additional random events.
You can even pair this achievement with