Your alien is related to the mantis shrimp.
They have the best eyes in the animal kingdom, with not two, but three pupils in each eye. Humans have binocular vision - we perceived depth by focussing two pupils on the same point. Mantis Shrimp have trinocular vision giving them better depth perceptions than humans using only a single eye. Not to mention that they see in the infrared and ultraviolet range and discern polarized light in ways that we can't. These phenomena aren't a result of multiple pupils, but rather because of a larger number of photoreceptors - twelve instead of the three that humans have. In short, their vision is something we can't quite even imagine.
They have other amazing qualities, like being able to create shockwaves underwater that stun prey even if their bullet-fast striking appendages miss. Oh, and the Department of Defense is studying the structure of its shell for the sake of designing better body armor. But I digress.
Correction by Samuel confirmed - their eyes are indeed compound, like those of insects, so their "pupils" that we see in the photo are an optical illusion - which I think is still pretty cool. Details in this article, which also tells how they can distinguish between right- and left-circular polarization of light, and may even use this as a communication method. Their vision is still trinocular, however, as each eye has three distinct sections.
I wasn't going to, but LSerni in the comments already did. Obligatory link to The Oatmeal, though the notion of them being able to see so many colors was disproved - many of the extra photoreceptors are used for some of the above purposes.