You need to beat each group of them at least one time. My advice is to pay attention to which of the enemy characters talk, since there are 5 different types / groups IIRC. I think the speech bubble for the group will turn grey if you've beaten that group, but not positive.
It's very much possible to do it, since I did it today on a fresh download of the game.
I don't think you have to do it in one day, since i was able to do the all of them one day and the boss the next. If you want to try for one day, get the sniper whip. Focus Jenna's attack and Jewel's attack ability to kill, with Throbb's attacks to knock them back if you can't kill them. Heal with Jewel as needed, remember that it damages her slightly healing other's, but can also be used on herself.