I haven't tried 3BP yet but do you have an AoE Lancer? I have my own Elisabeth and with Jalter they can end Ibaraki and the hands in three turns. Try Jalter + Waver or Hans + support Lalter. Build NP in first wave as much as you can. Deal damage to hands until they are half life each. Plugsuit backline Waver or Hans then Lalter NP + Jalter NP + Jalter crit.
How to raid
I can do 2 BP raids pretty well, but I can't seem to outlive the turns in BP 3 thanks to the arms' damage and Ibaraki herself. I currently have Mash to tank NPs and Waver to extend the turns by reducing charges with a neat chance to stun, but they still manage to kill me by the last 1-2 turns.
What is a good order of priority for raids? Kill the arms first or prioritise accumulating Ibaraki damage and hope to outlive the turns?
I'm using Jalter + 2 Wavers as front line damage dealers, with Mash, Hans and Jeanne D'arc as backline.
I say taking both of them out will be a good idea as to avoid being stunned/having your skills sealed on top of being a good source for the event currency. Note that eliminating both hands will allow Ibaraki to attack twice and if she gets a crit that servant is most likely dead.
I would also wait until you have enough of the damage boosting event CEs before trying to clear the 3BP raid. Once you have enough, bring at least one servant who has class advantage over Ibaraki's hands.
During the last few days of the event, both hands become Berserkers so by then you'll wanna focus on taking them all out asap with your strongest servants.