They should really make clearer that new players shouldn't focus too much on these progress missions. Everybody sees the legendary at the end so wants to move through the progress missions as quickly as possible, but that's really not the way to go. You won't get there until you've reached the end-game anyway (at which point a free Arbiter is nice but not game-changing as it would've been if you could actually get it in the first few months of playing). So along the way you shouldn't focus on the missions unless they align with something that helps you in other ways too.
In this case, you should be leveling up your food champions in order to get your starter up to level 60, or your next main champions if the starter is already there. Considering the progress mission, you can do the leveling up in a stage dropping boots - but the leveling up is what's important, not the progress mission.
The biggest bottlenecks in the progress missions, in my opinion, are actually the arena ones which require many hundreds and eventually thousands of arena victories - but then, you do need those arena victories to get to the end game, because you won't be strong enough if you don't properly develop your Great Hall bonuses.