Looking at your previous posts, you're using a balder side sword +6, which won't do too much damage against her. But you can farm the slimes in the swamp and bring your weapon to +10, it will make a big difference. That sword also scales its damage quite well with your dexterity stat, so putting more in that will add some damage as well.
Use the shit out of the sword's thrusting (R2) attack. You can roll through or away from her sword attacks. Don't get stuck by her legs. Either be attacking her human half after she misses attacks, or her back. You'll get used to her animations and know when you need to run away from the explosion attack, which is by far the biggest threat in this fight. I don't typically use lock on in this fight, I think lock on makes it more difficult to avoid her lava attacks.
She's completely resistant to fire so if you're using pyro or charcoal pine resin don't bother.
If you found the shadow set while exploring blighttown, that has high poison resist. You could make it to the other side of the swamp without getting poisoned as long as you let the meter drop down while you rest on drier ground. But, don't worry too much about getting poisoned. It's really not so bad fighting her while poisoned, the HP drain is pretty slow and you have time to run away and heal when you need to. Also, just run past the boulder giants on your way to the boss, they won't follow you into Quelaag's domain.
If you haven't, you can summon the NPC Maneater Mildred for this fight. You have to be in human form and she will invade, then when you beat the phantom you will be able to summon her by Quelaag's fog door. Watch as she walks into lava over and over again. But her weapon is pretty damaging and she's a nice distraction.
Also if you need to leave Blighttown to get more moss from the female undead merchant or talk to Andre, you can go up the waterwheel -> Valley of Drakes -> New Londo Ruins -> Firelink Shrine (it's a faster trek than all of those location names imply)
I'm using the Balder Sword +6 for certain things, but my go-to weapon has been the Halberd, which is what I've been using against the boss. I did try the sword once, but it was laughably ineffective.
I've got a pretty good grasp of the attacks the boss uses by now(it'd be bad if I didn't), but it doesn't stop me from getting fucked by some of them. I try and stay a distance from the sword slashes, then run to the side when it does the fire breath thing. Problem is, it'll often jump at me, which I can block, but it still does decent damage, knocks me down and back, where it'll hit me again, or I'm knocked into a pool of fire, which is pretty much my end. I've gotten it down to low health a couple times, but I feel its just pure luck in terms of having it do certain attacks I can get away from. Certain ones just screw me and I haven't figured a way to stop it from happening.
EDIT: I've tried the rolling away from the sword attacks, but I get hit like everytime. I dont understand how that works. I'm only a medium equip character so the rolls dont get me that far away.
One thing I haven't tried is not using lock on. It'd let me run away and to the side easier, but I think I'd get killed by the sword attacks pretty quickly since its hard to block without lock-on. Worth a try if I cant do anything else, I suppose.
Being poisoned is bad, actually. It'd be one thing if I could heal when I needed to, but I have to wait for the right moments to do it. If I'm low health and I'm on the defensive, I cant just stop and heal. Also, the boulder giants wont follow me into the domain, but they'll definitely kill me as I try and run past them. Tried that a couple times. The rock throws take away most of my life, knock me down, and get me killed.
I also cant surive in New Londo Ruins. I went down there from Firelink Shrine a couple times, but die within like 30 seconds from these ghost things I cant hit. I dont think going back is an option.
Really think summoning is my best hope. Can I summon somebody more than once?
EDIT: Gonna try a couple more times before football starts. Crossing my fingers. Also, thanks for advice. Souls community seems really good about this stuff. Its a fun game to talk about, I guess.