The Mantis Shrimp most likely sees very much like us (or birds, snakes), it's just that its brain is too small to integrate signals from just three types of cones, so it evolved a whole rainbow of cones.

This misses one of the best mantis shrimp facts.

One of its receptors only detects circularly polarized light

But the only thing we know of, in the entire natural world, that emits circularly polarized light... is the reflection off the shell of the mantis shrimp.