This spurred me to think about how you could detect X-rays, though.
X-rays get absorbed really quickly in things like water, so it'd be pretty hard to sense them directly with an eye like ours, but I can imagine a sensory apparatus on the skin or behind a thin transparent (to X-rays) layer that would detect them.
Another cool option would be to take advantage of all of the free electrons that an x-ray creates as it bounces around getting absorbed in a solid or liquid. If you had a sensory apparatus that consisted of a conductive liquid with a voltage across it, you'd generate a current whenever an x-ray hit. This is similar to how things like geiger counters work, although I doubt an animal would be able to generate enough voltage to create an avalanche effect amplification.
I bet there are other ways, but that's two off of the top of my head.