Play the Daily: Infernal Invaders with four human players. You will not have the choice to take food with you on the mission. There is no food available to be picked up during the mission. At the end of a successful completion, Kenny will appear and unlock the achievement if not already earned. I have done this three times in succession.
I would have waited and done further testing before posting this solution. I don't consider the test to be conclusive. All three instances were done on the 25 November 2018 daily. Another date may yield different results. However, many people are anxious to get this achievement before the 12 December 2018 server closure. So, I thought I'd err in favor of a quick posting. I would have done more testing but am having trouble finding three other human players to volunteer for the experiment.
When I first played comrades back in November 2017, I relied on a random appearance. I got all chefs except for Gentiana and Aranea before Kenny appeared. It took me over 40 hours of play. I tried all the missions several time varying food choices. There was some discussion about what missions and food choices were best. They may have improved the odds but none of them worked for me. Eventually, I got it while grinding and did not take note of my food choices. Since then, Kenny has appeared only half a dozen times. He has appeared in both low level and high level missions. I have been unable to discern any pattern other than the solution I posted above.
Edited 8 Dec: I have now tested with a party of 4 human players over a dozen times with 100% success. When we started any mission the Dailies, an urgent mission, or a regular mission with no food and picked up no food on the battle field, Kenny has always appeared following the mission. With the Dailies, human players start with no food and there is no food on the battle field. So, as stated above, Kenny appears after the successful completion of a daily mission with 4 human players. If the human party of 4 plays an urgent or regular mission (red or green missions), and ensures nobody picks up food at the camp or on the battlefield, Kenny appears following successful completion of the mission.