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I don't think you have missed anything, but I think you're supposed to get magic from the turnip, not a sword. Did you get to choose what you want? If you are doing decent damage to the slayer (about 10-20) I don't think there is anything you are missing. But, with the turnip magic instead of the sword, the fight is fairly straightforward. Also, from the (I think) merchant in Nowheresville, you can buy a piece of metal that you can use on the hole in the wall just before the slayer room. It gives you a second chance of fighting her if you fail the first time, but that doesn't seem very useful, not unless she remains at the health you beat her into at the first try (I never had to retry when using Turnip magic, so I'm not sure).