360 view doesn't mean good eyesight. For instance, a spider has a pretty wide field of view, but it sees mainly in infrared, meaning it's vulnerable when the predator has a low body temp, or it's skin is a bad heat conductor, meaning it gives off low heat.
In my mind, in a planet where there isn't blind spots in eyesight, camouflage would be key, and so, predators would evolve to become extremely apt at blending with the fauna or soil, color changing skins, props that would look like leaves, or tree barks, skins that look like sand or snow, and so on.
That would give you a good creative margin towards creating diverse means of camouflage, from "passive" to "active" means.
Otherwise, speed and agility would also be key, with the fastest predators being able to ambush more effectively their prey.
I also think when in soft soiled environments, like a sandy desert, tunnelling and vibrating sensors would be key, since all the field view in the world won't make you see through soil.