How to deal with Arthur's long range assault in MVC3?

The most important thing against level 3 X-Factor is to not get hit at all costs. If you still have two or three characters with a good portion of life, then just blocking is definitely a better alternative. Super jumping up-back will help avoid a good portion of the chip while you wait for the X-Factor to expire. And as Wilerson points out, you can X-Factor yourself to not take any chip. Then he'll be forced to do something else because spamming projectiles will do nothing.

If you have a character with flight on your team, you could also fly as high as possible to avoid things. Just be careful with this, because you can't block while in flight.

Many hypers will outright beat projectile spam. For example, Dormammu's Chaotic Flame has very fast startup and can punish Arthur projectiles on reaction. Similarly, Ryu and Akuma can use their beam supers to punish. Magneto can do his level 3 Gravity Squeeze from anywhere on the screen in reaction to almost anything. This will not only take off most of his life, but allow a good chunk of the X-Factor timer to drain.

You could also use Amataresu's shield (dragon punch+C) to reflect his projectiles back.

If you do decide to approach, remember that you can block even while jumping forward, and you should definitely do this if he's spamming things while in X-Factor. Super jump forward, then go straight to holding back.

The key is to be patient, don't press buttons randomly (you don't want to get hit while he has X-Factor), and punish projectile spam using super if possible. After a few punishes, he should be a little more hesitant, and you can actually get on with your normal gameplan.

Arthur is weak at close range and can't backdash. So, your best option is to use a hard-hitting character and get in. Captain America's Charging Star (especially the Hyper version) is great for this. When you get in, try to land your best damaging combos. When Arthur is in his underpants, he receives 30% more damage.

EDIT: Another good option is to activate your X-Factor too: you don't receive chip damage while in X-Factor.

Hsien-Ko easily beats Arthur if you spam Gongs (reverse dragon punch + any) or properly time some Gong assists. Hsien-ko can also throw other projectiles with a chance to dizzy.

Ammy's shield is is OK, but seems (to me, anyway) to come out a lot slower. You can alternate between reflector (22A) to use the shield and beads (22C) to fire puppy lasers... err, ice beams. The 236C version of ice beams has a 45 degree angle that can keep you safe from some projectiles.