Anyone else think SE got a different person to voice Jihl? That doesn't sound like her at all...or maybe I'm just completely wrong on this. Oh well. (Sorry for the tl;dr...I can spoiler this if anyone wants)
Fighting Jihl is awesome. The fight is just so hectic and challenging but I think I've got a fairly safe strat that takes her down well enough. Since it takes so long stagger her and she can heal herself with her minions, the key is to down her the first time you stagger her.
Depending on my luck (ie how often the character I'm using gets thrown into the air...) this fight takes me anywhere from 5 minutes to 6 minutes. Either way, that's a five star so I'm happy. So here's what I do:
Paradigm Pack (MED/SYN/RAV) Basically I use Lightning, Sazh, and White Chocobo (though I don't really use it much...but for safety it can't hurt)
Paradigms:
SEN/SEN/SYN
RAV/COM/RAV
RAV/COM/MED
RAV/RAV/RAV
SAB/RAV/RAV
SAB/RAV/SYN <-- Your starting paradigm
Equipment: Whoever is going to be your SAB should have the item that increases SAB role bonus (I forget what it is right now...sorry v_v), something that boosts MAG and the Grimoire Hat. Ideally, go with the Grimoire Hat over the MAG boosting item if you can't wear all three. Make sure to have a lot of potions. You will need them for consecutive battles.
Start off immediately with just casting poison. Just do it over and over and over again. Switch to SAB/RAV/RAV every other ATB recharge for a quick refill and to help up the gauge even quicker. About 10 seconds after Jihl uses Sneer, just switch to SEN/SEN/SYN and heal up your HP for the oncoming onslaught. Hopefully by then, your SYN will have given you all protect and shell. If your SYN dies because they were targeted, just raise them and head back into the fray.
Poison just DECIMATES Jihl. My last fight it took her down all the way in about 2 minutes before I could even get her to stagger. It was insane. If it wears off, just apply it again. That's why you should just focus on getting Poison on her. (TBH I haven't tried a method with alternating Imperil and Poison yet but that's next on my list to see if it'll quicken the kill speed)
Heal up as necessary throughout the battle. Just guzzle potions. They are more effective than a MED with the Grimoire Hat at this point anyway.
One thing to keep in mind, once Protect and Shell are all on your party members, you might as well switch to RAV/RAV/RAV and SAB/RAV/RAV to get the gauge up quicker. Just keep an eye on your buffs.
Once Jihl is brought to stagger, switch to RAV/COM/RAV and take her down. If you're controlling Serah, use her Ultima Arrow before switching to Noel. Once Jihl's at 999% and the stagger is about to die off and she's not dead yet, use Meteor Javelin. That should finish her off. If not...you might as well restart the battle.
Once she's down, kill off her minions. To save on potions, just use RAV/COM/MED to take them down and heal up HP so they can't harm you. They are pretty easy, anyway.
The biggest annoyance in this fight is the minions ability to knock you into the air
Stupid Aeroga. That can eat up some time. Hope this helps anyone who needs it ^^
Gonna continue finetuning this tomorrow, but for now this strat works great.
Now if only Jihl actually dropped gil....