Little tip for you, you can still damage a dying king while it is in its deaththroes (the explosion of light they do as they're dying). If you hit hard enough and quick enough it can actually shave off an entire kings worth of health meaning you'll only fight 3 kings.
Yeah. Just can't kill them quick enough. I use Power Within and nail the first two pretty quick, then wait ages for the third, by the time he arrives my power within is wearing off and although I can usually kill him the fourth king nails me.
Having a break from it now. Will prob try again in a few days. I can definitely do it, just being sloppy with the fourth king, but I'll get there. It's not frustrating, just requires a bit more skill than the first run through!