From the thread on astrobiological arXiv papers comes this thread:
Could an alien have the equivalent of a human eye that covers its entire body?
Well, you have heat sensors all over your body as a human, which isn't quite the same but can start the issue. I'm trying not to think of a creature like the mythological giant Argus, covered with real eyes. An undersea creature could have pressure sensors all over, so it picks up indications of nearby creatures.
(art, not mine, shows Hera ordering Argus to guard a white heifer)