The easiest way to cheese this achievement is on Judgement.
Make sure your deck is loaded with Gladiator's Visage, and try not to have any other helmets. The game gives you a full set of randomized equipment loaded out from your deck at the start of the challenge, so you should have the helmet if it's the only one you put in. When you get to the second or third floor of the challenge, you'll run into silver tokens of the Empire, which initiate combat. These tokens respawn endlessly if you wander around the map, and if you do the combat flawlessly the maps seem to always give you 10 food for a reward with Gladiator's Visage. Camp out their spawn locations, and keep walking on encounters you've already cleared, and you should be able to reliably farm food until you get to 300.