No point using any other magic than fire staff if you're on your own. Depending on your elemental skill, you might want to bring a spare staff, especially if you forgo use of bow entirely.

Frostner is useful for dealing with regular seekers and broods, I prefer the knockback over Mistwalker's raw damage. You can also dispatch swarms with bile bombs to save your magic resources (and staff durability). You need good skills to be able to take out extra enemies quickly and to maintain distance while running the stairs, so you'll have to bring more potions the longer the fight goes on.

Eikthyr buff might be the best choice there, but Bonemass can be safer at the beginning before you've managed to climb the stairs.

Feather cape is essential in the battle in order to escape and put distance between yourself and the boss. I also used root harnesk, it can help mitigate some manage from seekers. You could also do with fenris set but I don't think the speed increase is worthwhile in place of better armor or eitr regen.

Made a recording of my lengthy solo battle here, but there isn't anything special about it: https://www.youtube.com/watch?v=fe4vz7v2Ccc You can see I had wrong food there in the beginning, 1/1/1 split for all stats should be optimal when using fire staff as main weapon, I went with two for health instead because I was uncertain of her attacks. You could use two health foods with one stamina and use a bow until you can change food, so you are not in as great danger until you've made it to the stairs.