I got in a chunk of battles this afternoon. Might try for some more tomorrow, but also might not.
ETA: Woohoo, we won! I will crack a cookie later tonight.
Day 1: Earth (Magic Vial) --> Grey (Puppyblew) -> Dark -> HP+3 to battle pet (that turned out better than it could have)
Day 2: Battle (Gnorbu Jockey Riding Pants & Boots) -> HP+3, Str+3, Def+3 to battle pet
Day 3: Water (I forgot to pay attention) --> Water (Cybunny Down) -> +3 Def to back-up battle pet
Day 4: Air (Peppermint Toothpaste) --> Soup (Large Cucumber Breezes Smoothie) -> +2HP +2Mov to battle pet
Day 5: Fire (Flower Purse) --> Battle (Brians Guide to Winning Gormball) -> HP+3, Str+3, Def+3 to battle pet
Day 6: Fire (Moehog Card King Sword) --> Soup (Small Blueberry Tomato Smoothie) -> +2HP +2Mov to battle pet
Day 7: Earth (Nanka Bottle) --> Light (Lady Osiri) -> +2Lvl to battle pet
------
Day 8: Grey (Spyder) -> Dark -> HP+3 to battle pet (woot, another good result from Grey!)
Day 9: Soup (Large Bean Smoothie) -> HP+2, Mov+2 to battle pet
Day 10:
5 of 6 refreshes for stats that I wanted (HPs and Level), and the day I didn't refresh gave HPs. Definitely worth it! (+13HPs, +2Lvls)
Hopefully the remaining days will give good quests, too.