Context :
My question: how would creatures of this planet hunt? Would ambush hunting ever evolve at all?
Just the way they do in our world.
If you look at herd animals for example their eyes are at the sides, giving them an immense visual range where they can pick up and spot movement.
The way around this is essentially speed, ambush and sometimes a bit of teamwork.
Speed lets you accelerate to the prey and hopefully overtake them.
Ambush lets them surprise prey from some type of cover. Speedy hunters will "ambush" by first getting closer, reducing the distance they need to sprint to catch their prey and reducing the time prey has to accelerate to its own maximum speed.
Teamwork lets groups single out prey from groups, or cause them to run in the direction of others of your group. This is where humans get their first mention.
Bonus: endurance. Humans might be the only species to have used this. They will jog up to a prey animal, which will scare and run away. After a distance the prey thinks its safe and stops running, but then the humans overtake it in their jog and it runs away again. Humans are better at releasing heat and have more endurance muscles. The prey will exhaust and overheat, then be easy to overtake by the humans.
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.
I don't see that big difference with respect to our real nature.
Most preyed upon animals have an already large field of view, and yet they fall prey to their hunters.
Ambush attack, mimicry, velocity, endurance and so on are all factors that weigh in when it comes to deciding the outcome of a predator-prey encounter. Predators would improve in some other area if prey have an edge in detecting them.
Actually, the prey and the predator not only have the same relationship as in our world (mentioned in the other answers), there is one more interesting thing:
Visual bandwidth limitations.
Looking around with 12 eyes, each one of them with its own high-precision spot, maybe eyes hardwired in pairs in order to get 3D vision (or paired randomly on as-needed basis) is quite a computational task.
Even having only 2 eyes, our vision uses a significant part of our brain volume.
Those with 12 eyes of comparable precision will be limited not by their optical organs, but by their brains.
They will have "neurological blind areas" with convoluted, but somewhat predictable behavior. Predators (especially in a group) can abuse these areas for their advantage.
The prey will evolve more powerful brains and more complex blind area mitigation strategies in response.
The prey may as well evolve behavior patterns that overload the predator's visual system.
Quite likely how most hunting is done on our planet already.
It is one thing to be able to receive sensory input from every angle and quite another to process that sensory input simultaneously in real time, allocating 'processing time' to all angles equally.
Good vision is already quite an expensive evolutionary gadget. Take owls, for example. Their nocturnal, binocular vision is superior to that of most other birds of prey. The price? Owls are dumber than a second coat of paint. Their vision takes so much of their brain's processing power that there's little left for anything else.
And so, it feels quite implausible that the 360-degree vision would be a game changer for prey - it would necessarily either sacrifice vision quality, or the brain's processing time allocated to other tasks, like planning an escape strategy, movement coordination etc. A more evolutionarily stable approach seems to use a wide-angled visual apparatus for motion detection (in which case poor resolution is more than enough), and then rotate your head towards the source of that movement to inspect it, putting it in the part of the visual system where an animal's sight enjoys the best resolution. Indeed, this is how the visual system of many prey animals already works and, as other answers pointed out, many of those animals already have quite a large visual field, no need for extra eyes, mind you.
Whereas for predators, the extra eyes would likely devolve. There's little need for predators to pay close attention to their surroundings - when hunting, they literally need to have their eyes transfixed on one object, and one object only. Anything but that would be energy-inefficient.
At night, by smell. Multiple nostrils provide directional information. And simply travelling upwind will lead u directly to your prey as long as you don't lose the scent too long. If the wind changes a bit of direction or ground features it might need to move its head around or zig zag a bit. Wolves and dogs do this all night, even in the day because food is smelly and using wind flow one can see through and around obstructions to light.
The natural selection developed a new kind of specie in this world:
The predator eats eyes.
The predators can be tiny (like ants), or tall with a pointed beak (like ibis). The carrion birds/crabs/slugs take care of the rest.
