What level is your Anya?
If sufficient, I think she might be able to hold out if you use her skill during the final phase, especially if you bring a lightning rod in the melee slot below her to draw away the attacks from the mages. There's also enough time to place a Priestess Warrior in the melee slot behind Anya's spot also, who could help shoulder the healing burden. I use CC42 Ertel for this, myself.
For the frontline I'm using AW72 Sybilla (2254 HP, 536 DEF after buffs) to take the Prince's place and AW68 Sophie to serve as a lighting rod. Based on the damage Sophie takes, I think that Niel might be able to serve if CCd. If not, I hope you were able to get Erun from the new year gold rush event. She'll get the job done. Valkyries or Bandits could too, but they'll start picking fights with enemies that come near~
I have not been using AW Katie or AW Aria for additional buffs in my runs. They'll definitely help if you have them. Also note that with this setup you won't have enough deployment slots to place the mage that is placed near the end of the video, but Bashira and Spica can handle it if they're high enough to one-shot the flyers.
