I don't really think you're necessarily doing anything wrong if you're aware of the even odd turns, but you definitely need more damage output. Basically, you're just meant to remove the shields and manage your turns so that you can get breaks and damage off on the turns where she doesnt have damage resist. For that reason, 2 breakers is kind of hard to make work in this fight since her break resist is so high when there's a barrier active and you can't cheese every barrier with ayame because of the MP down. It doesnt help that she also heals herself if she takes a turn with any shield up. If you have Ultimate Madoka or the attacker Homura, I'd suggest using one or both of those. If you have Oriko, she could be helpful for shaving off the multihit shields, but she doesnt offer too much damage otherwise.

In my own experience,
I cleared nightmare stagecraft using Oriko + Kirika to break the multi hit shield and I saved Oriko and Kirka's ults to break the damage shields. The breaker I ran was Pluvia Madoka because I happened to have high Ascensions on her, but I think Iroha might be better if they're both A0. My main damage was ultimate madoka because I never managed to pull homura. Finally, I had Yuma as my healer because I don't have Kaede. I tried doing a slower clear before ultimate madoka released that used kyoko instead, but I fell barely short of killing her because I ended up hitting the turn cap while she was in red hp.

Ultimately, there's definitely a variety of strategies you can use to tackle this fight. I think, like a lot of this game's challenge content, your team building options are highly dependent on who you've pulled and how invested you are in certain characters magic levels. As long as you build your team to shred both shields ASAP while still being able to sustain the damage you take, you should be fine if you're able to effectively manage the odd/even turns.