This battle goes a lot smoother if you have a long-ranged weapon. The spider has three attacks. First, it can spray three huge webs across the building. Immediately after firing those webs, it will either charge and fire a fireball at you, or run at you in order to slash you. That's basically all it does. The webs are usually more annoying than dangerous, and as long as you keep your distance you probably won't get hit. The fireballs are easily dodge-able as well, since the charge time gives you plenty of warning. The trouble starts when you actually try to shoot it. If you're using anything less than a rifle, you're going to have to be dangerously close to that quick slash it has.
After you deal about 450 damage, you'll begin part two of the fight, which is the same as part one, it's just played out on a different section of the rooftop.
It should be noted that Aya technically never defeated the Spiderwoman in either of the two stages it was encountered on the hospital roof. After Aya escapes the roof on the scaffold, the Spiderwoman breaks through a window and attacks the break, sending Aya and a Spider NMC down to the ground. It's possible though that the Spiderwoman died of injuries inflicted by Aya, or that she was killed at a later time by Aya returning to the hospital or when Eve was killed.