This is story related, and cannot be missed.
Compared to previous battles (even the previous face-off with the Second Sister), this is probably the most difficult fight, up to this point. Keep in mind, I'm playing on the penultimate difficulty (next to last) because I enjoy the slightly more challenging gameplay, and I'm writing this very soon after finishing this fight. So I don't know if things get easier or more difficult toward the end of the game.
This is what I noticed, what worked for me, and what I recommend; YMMV.
At the beginning of the fight, the Ninth Sister uses a single blade on her lightsaber. I recommend matching what she uses, as a single blade seems to offer more speed and precision, which will help against some of her attacks. Speaking of attacks, she's fairly slow and tends to telegraph her attacks pretty obviously (for now; more on that later). There's a standard saber strike combo that she does with three swings that are pretty easy to parry. Parrying is key, here, because it wears down her guard (a thin white bar, much like your own "guard" or "blocking" bar on the HUD). However, every now and then, she will interrupt or end the combo by turning red (you should be used to this indicator, by now) and delivering an unblockable attack -- usually a long distance stabbing lunge. The only way to avoid damage from these is to roll out of the way. Any time she does an unblockable attack, you have a small window to get a couple of hits in. You can go for some plain saber attacks, but sometimes your roll will put you pretty far away from her. I recommend using the Dash Strike (especially the Improved version), as it closes the distance quickly, and does good damage. It uses Force, so any skills that help your Force stay charged are also recommended.
Sometimes, she will Force Push you away to prepare for an unblockable leaping slash. If you are not ready for it, the Push will knock you off your feet, and make you vulnerable to the imminent attack. If this happens, try to evade/roll in order to get back up quickly. However, if you are blocking, the Push will make you slide backward, but remain standing. Then you can roll out of the way when she leaps toward you, and then counterattack.
There's one more unblockable attack that she will use here, and that's a running charge that hurts bad. It's faster than it looks, and you can't roll out of the way at the last second. You need to roll earlier than you probably think. Then she'll be open to a counterattack.
You want to get as much damage on her as you can, any time there's a window of opportunity, but make sure you learn to avoid and counter each type of attack. You'll need those skills for the next part.
When you get her health bar down to the right side of her name (not quite halfway; maybe 1/3 or 2/5), you will probably trigger a QTE; you just have to mash one button repeatedly, and it was always 'X' for me in this first sequence. When you remove more health down to the left side of her name (maybe another 1/3 or so), another QTE is triggered where you mash the 'B' button.
Now is the hard part. After that first QTE, she will switch on the other blade, and I recommend you do the same. So now it's a double-bladed lightsaber battle. These double-blade attacks are more powerful, and seem to be easier to parry if you also use double-blades. Earlier, I mentioned that her attacks are fairly slow and it's easy to tell what's coming. Well, now they're faster. And she can spin her double-bladed lightsaber like a propeller, so that's fun. Some of these unblockable attacks have such a wide damage arc, long reach, and fast speed, that it can feel like you have to roll multiple times to stay out of the way, with no window to counterattack.
Well, I lied earlier when I said rolling was the only way to avoid them. Force Push and Pull can interrupt her unblockable attacks, but I didn't find that very useful as it provides no window to attack, and now you've used up some Force. The Force Slow skill, however, lets her continue the unblockable attack while you casually stroll (or roll) around her, and attack her from behind. I was using the Burst Slow (upgraded form) since it slows the target for longer, and it seemed to work well. This is especially useful for an unblockable attack where she spins the propeller blades at you in a far-reaching lunge attack. Watch out for the reach on those spinning blades, though!
Keep the Slow skill in mind for healing, too. I can't tell you how many times I called for a stim-pack, only to have her rush in and punish me for it; either negating the stim-pack I just used, or hitting (and killing) me before I could heal. I finally learned to only heal after using Slow.
As for the rest of her attacks, most of the attacks from before are back, but they're faster and harder to anticipate. She also has some new attacks. There's a ground-pound attack that is heavily telegraphed and easy to see coming; just double-jump over the shockwave (dirt-wave?). There's also an addition to the running charge. If you roll out of the way, she will skid around, regain her footing and charge again. It's faster than it sounds, so be ready to perform a second roll/dodge.
Finally, there's my favorite attack: A fairly obvious lightsaber throw. Now you can easily block this, and it seems inconsequential, but if you learn the timing, you can PARRY the lightsaber, which sends it back at her and causes a chunk of damage. Very nice.
On the difficulty setting I chose, this felt like the first real challenge-hump to overcome, so it felt really good to come out on top. Keep at it, and keep causing damage (but don't get greedy!), and sooner or later, this fight will be over. Congratulations! (or Good luck!)