Okay, the trick for that fight is to take out the left or right doll first, then the other. Alice herself doesn't start using dangerous skills until the Healer is taken out. This may seem impossible, however, the Magic doll is weak against physical attacks (Chen, Youmu, Remilia, Sakuya, Cirno's Diamond Blizzard, Meiling), and the Shield doll is weak against magic attacks (Marisa, Patchy, Rumia, Minoriko).
Deal a few thousand damage to whichever you target first, not enough to make the Healer use the 10k heal on it though. Then, right after the Healer takes it turn, have as many characters as you can use an effective skill on it and kill the doll before the Healer can heal it. Then, repeat the strategy for the other one. Afterwards, wait for the Healer's buffs to wear off, and it should be an easy kill, then you just have to tough out Alice herself. She isn't too hard with no dolls left supporting her.
Meiling's Healer skill is great on characters with a status effect, and its useful to have her cure Remilia's Curse of Vlad Tepes side effects right as the battle starts. Until I dropped Meiling for a better tank, I always started boss fights with Remilia cursing and Meiling curing it.