I beat him. I went back to my tower, made a lot of 200+ healing potions, put those on Dragon Hotkey 8, allocated a point into Dragon Shield and Dragon Blast, and did a lot of quicksaving. It still took a few tries, though.

After that I hit level 26 and decided to try Stone's Flying Fortress, and I discovered that they are MUCH HARDER than they were before. But I got 4.5 levels out of it.