As with every achievement in Edurance mode, first select the challenge before starting the game!
Bears will appear regularly from day 3 onwards. They are best killed with poison or fire arrows. The important thing is: when eating the bear, make sure both of you are standing close together! Only this way both of you are eating at the same time.
If one of you is too far away, just the player who eats the bear will gain food from it - and it doesn´t count towards the challenge.
Repeat this three time and the achievement is yours.
As a sidenote: it doesn´t matter who of you is selecting the challenge, both players will get the achievement after eating the third bear.