IMO the reason we don't see more two weapon fighters is because our brains are not sufficiently parallelized for calculating the motions of two objects at a time. Putting this in simpler terms, adding the second weapon decreases our effectiveness with the first.
I think increasing the number of arms to 4 suffers from the law of diminishing returns. In most cases, without special training, just using 3 shields and blocking as many directions as possible, while your primary hand wields your weapon will be the best fighting technique.
I've actually fenced competitively. Once I start a lunge, I've already decided all of my measures and counter-measures. I go through them as fast as I can without awaiting response from my opponent. I use the time in-between attack and perry to analyze what I and my opponent have been doing and are likely to do and try to figure out my next attack and defense combinations prior to the next engagements. I do not know whether high end fencers do this the same way or they are able to react to the actions of the other fencer in real time.
Someone who spent years trying to master multi-armed combat might be able to do better, perhaps much better. Even if she couldn't, if she could master a series of automatic attacks and defenses with 3 arms with which she'd simply use muscle memory to control it would provide her with a big advantage.
Meanwhile she could concentrate on the attack and defense of her main weapon.
Fighting someone like this
As someone who would have to face her, you would need to worry about what all of those "automatic" arms are doing because they can still harm or kill you. Even if they're not a huge threat (compared to her primary weapon), they'll still be a huge distraction which probably gives her primary attack (her main hand) a huge advantage.
Some fighting styles
- 2x Shield and sling
- 2x Bow and arrow
- 4x Handgun
Just remember you'd have difficulty aiming more than one of these at a time. Although especially for the primitive ranged weapons, she could spend all of her thinking doing the aiming and then using her arms to bring the next weapon into the ready position - almost doubling her rate of fire.
- 1-handed weapon (main) + 3 shield
- 1-handed weapon (main) + shield and 1-handed weapon + shield
- 4x 1-handed weapon (main)
- 2-handed weapon (like spear/pike) + 2x 1-handed weapon (main)
- 2-handed weapon (like spear/pike) + 1-handed weapon (main) + shield
Note that there's always a (main) weapon. This is the one she spends the most time thinking about and using to react to her opponent. The others she'll use reflexively to block blows or occasionally take advantage of an opening.
I think these last two combinations could be particularly deadly. You hold back on the spear, fighting mainly sword + shield. When you're opponents backs up for a short breather and provides an opening, you have the range to suddenly jab and attack that opening.
It would probably quite deadly to those not used to the technique.
I fenced right-handed. My roommate fenced left-handed (because he was left-handed).
He loved fencing right-handed people because they were used to fighting right-handed people and they were unfamiliar with left-handers. He was used to fighting right-handed people and almost always won in such matches.
I hated fighting left-handed people for all the same reasons.
In your Universe, it might be the same for your protagonist. For people unfamiliar with her style of fighting, she'd be extremely deadly. Meanwhile, if she hasn't been around any of her own kind for a while, she might suffer problems when she's faced with fighting others like herself.