Darkest Dungeon

While walking in a mission at random your heroes will get hungry. A pop-up will pause the game for you to decide to eat or starve;

Press to eat press to starve. Note that if you have no food on you, you can only starve.
When you eat, you’ll use food and all heroes gain HP (5% of your total HP).
When you starve you’ll not use food but all heroes will suffer 20% max HP damage and 20 stress damage. If this HP damage gets you killed, the trophy will pop.

Note that if the stress damage makes you reach 200 and the hero suffers a heart attack it will not count for the trophy.
Note 2, heroes won’t starve if they have -100% food consumption buff (like the buff from the Bloodthirst Ring).

Choosing to starve with 0HP will not guarantee a death, as you still have your Deathblow resistance to take into consideration, so it can take multiple tries to die from hunger. If you farm for it, you can simply keep walking up and down the same hall till the party gets hungry, choose to starve and hope. If no one died, walk more.