I'm not a fan of Janissa
for all the reasons pointed out. However, even the parts I do like (her being more skilled than Conan in swordplay, strong as a man, etc) I dislike, because it takes a lot of Valeria's thunder very early in Conan's career. I definitely feel there's room for more warrior women than just Valeria in the Hyborian Age (within reason: it would be incongruous to have dozens of them, otherwise Valeria's uniqueness is lost) but at the same time, it would be good to make her distinct in some way. So here's how I'd do Janissa:
Janissa was born to a wealthy Zingaran family. She rejected the courtly lifestyle set forward for her, always at odds with her father, who wanted to marry her off to a powerful nobleman. She secretely trained with a sympathetic Zingaran sword-master, and learned much more than she was supposed to: politics, history, her family's dark past involving a mysterious "bone woman." She started to make subtle power plays against her father, manipulating events and circumstances to undermine him. Unfortunately, her father discovered her schemes, and punished her by killing the sword-master in a rigged duel (poisoned blade, etc) for her "honor," and had the servants who aided her beheaded. She swore to kill him for this, but her father was a powerful man, and she could not sway the loyalty of his guards, vassals and knights. In desperation, she seeks out the Bone Woman to enact vengeance. The Bone Woman teaches her terrible dark arts and combat skills, imbuing her with terrible vitality, giving her the power to destroy her father - but at the price of servitude, and the cost to her soul which all dealings with black sorcery demand. After Janissa slew her father, the true magnitude of her choice was revealed, as the Bone Woman ordered Janissa to wipe out her entire family, leaving no trace of her bloodline: she was to torch her home, destroy all her possessions. There would be no evidence that her family ever existed. When she killed her domineering father, she thought she would finally be free, but she realised that she had simply substituted one cruel master for another, one more terrible and monstrous. And now Janissa became the agent of a monster.
This way we still have the dark side of Janissa's past, but desperation and rage drove her to make a veritable deal with the devil. I never bought the idea that Janissa would have to resort to sorcery just to learn how to fight, otherwise, how did Valeria manage? Similarly, none of that demon business: I fail to see how that could possibly be an effective warrior training tool. True, there might be a bit much of Dark Agnes and Bran Mak Morn in there, but that hardly stopped Busiek borrowing from Red Sonja, and most of those things are fairly universal, and I feel different enough. There'd also be some history between Janissa's family and the Bone Woman beyond their present circumstances (she might be a distant ancestor, or have helped her family gain their power in the dim past, whatnot), strengthening the link.
Also, she'd have a different costume.
That's just silly. I actually think it would be better for her to be topless than to constantly be on the verge of falling out of her top in a combat situation.