Arthur's main Artifice is her backmost stop. Cast as an ending act, it stops the target for two turns (but since it occurs at the end of a turn, this stop only takes effect on the subsequent turn). Once below 50% HP, she also employs a front 2 stop which throws a wrench in certain strategies.
Her secondary Artifice is her counterheal. While more for thematic reasons than anything else, this counterheal is just something you'll have to put up with, as there aren't any ways to remove it.
The natural counter to Arthur is 4★ Ryugu Dancer Ichie, a powerful Snow chopper with a Stop Resist passive, who always stands backmost. The stop can also be taunted, or blocked with any Negative Effect Resistance. Many of the strategies below will detail workarounds that do not require this Ichie's help, as Arthur is not too much trouble with her.
1) Standard Team
There are dozens of permutations to this team, and that number will only grow as more snow girls are added to the game. Essentially, all this team requires is one 4★ snow tank, Ryugu Dancer Ichie, and three of the player's strongest snow units.
Powerful snow units like Marie Kaoruko, New Year Tsukasa, Match Girl Yachiyo will make the fight go smoother, but for those without options even 3★ Sun Nation Futaba is passable, though the success rate might decrease.
Simply Ryugu Ichie + Match Girl Yachiyo 2girl can clear the boss.
2) Absorb shenanigans, again.
If you are not in possession of a 4★ Snow tank, this is a workaround. With some Unit Skills to buff Ichie and Drakuro (consider the back global Unit Skills as well), they can maintain a tenuous equilibrium for the first 50% of Arthur's health using Drakuro's 3AP, either Ichie's or Drakuro's 2AP, and then Ichie's 1AP, depending on who is more in need of healing.
Do not use your climax ACTs yet. Activate your CX when Arthur is more or less about 55-60% HP, and try to wait until the second turn to bring Arthur below 50% with Ichie's nuke. It is important to minimise the time spent fighting Arthur once she is below 50% HP.
In this phase, only use Drakuro's 3AP. It is a bit of a gamble to see if Arthur will choose to use her Front 2 stop move as the first move of the turn, but the odds are in your favour. Follow up with two Ichie moves. Once Drakuro is down you should have enough time to nuke down Arthur with Ichie.
3) Violently Exterminating Arthur (3 turns)
The only girls who need to use their climax are Fishchie, Stage Girl Junna, and Christmas Yukko.
To facilitate this, use Yukko's 4AP and Junna's 3AP charge to ensure that all three are necessarily charged. By being in the front 3, Yuyuko and Junna also charge from Arthur's whacks. This tactic takes advantage of Junna's starting dexterity buff, and thus the climaxes must be used on turn 3.
This strategy is used in the Lancelot Rotation Speedrun video linked below.
1) Viva la Britannia!
The queen everyone knows and hates is so good at her job that even with the disadvantage of a stopped backliner, the team can pull through (sometimes). It's important to use all the Marie moves you can, especially barriers.
Alternatively, use Siren Akira + Marie. Siren must be rank 9.5 with all defensive panels unlocked, unless she has high unit skill levels. Utilise a critical damage memoir on Marie, and a fully defensive memoir on Siren. This method is also not completely reliable due to Arthur's fourth Normal Act, but fares better than a full team. It goes without saying that only Marie's moves should be used. Hold one of Siren's cards and discard it the turn before Marie is ready to CX.
2) Hot Potato Stop
Suppose you have Match Girl Yachiyo and one other neutral element taunt tank (or Lancelot). Well, you can pass around that stop with taunts, which allows you to have your backmost girl unstopped and active. This type of comp should be done as a 3-4 girl group, to ensure reliably drawing taunts. Save Match Girl Yachiyo's taunt for Arthur's CX turn, which will effectively negate it. This means, of course, that she can't be stopped on that turn.
To accompany the two tanks, you'll need very high damage or a girl that can do damage and provide sustain support to the tanks. These are Marie Kaoruko (high damage) or Diaochan Ichie (sustain + damage from burn).