TL;DR Evolution is unlikely to come up with one solution to a problem, but rather a varied seletion of species which each try to solve the problem of survival a different way.
That's already the case for real life. Every type of animal in existence has a different genetic feature set, each of which is a different solution to the problem of perpetuating life.
This immediately reminds me of the Vashta Nerada from Doctor Who. In short, they are flesheating creatures that live in the shadows. I do suspect that your shadow creatures are less seemingly-omnipresent than the Vashta Nerada, but this is a good starting point for inspiration nonetheless.
How would the animal world adapt?
At some point during the episode(s), the Doctor specifically mentions that the Vashta Nerada are why creatures are conditioned to be afraid of the dark. Being afraid of the dark is a common fear, especially for children and some types of animal. And it makes sense from an evolutionary perspective, as it is pure darwinism:
- Those who are afraid of the dark will go out in the dark less than those who are not afraid
- As a result, those who are afraid of the dark will be killed less (by the Vashta Nerada).
- As a result, they procreate more often than their peers who are not afraid of the dark.
- Over many generations, an innate fear of the dark is bred into the species. They no longer know why they fear the dark, but their instincts are set in stone.
- This fear is instinctive, but it can be rationally overcome, which is why adults can lose their fear of the dark if they consistently do not observe any negative consequences from being in the dark.
This is already the case. There is a logical reason for our instincts to tell us to be afraid of the dark: you can't see it coming ("it" being whatever is going to imminently kill you).
The only difference between your world and reality is that the cause of death is a "shadow creature" instead of just an "unseen danger".
There are many other rational instincts whose justification is similar: fear of heights, fear of being alone, fear of animal howls, fear of being around dead bodies, ... ALL of these situations are situations in which you're more likely to die soon, and thus we instinctively learn to avoid them.
Could organisms adapt to emit light or would they have to rely on lantern and torch light?
There are many ways to evolutionarily solve a problem.
Bioluminescence is one such reason, but it's a rather intricate one. The more intricate solutions tend to be less likely to emerge. There will be some species that evolve into being bioluminescent, but it won't be ubiquitous.
You haven't really addressed any other weaknesses of the shadow creatures, so it's hard to tell you what would counter them. I'm just going to invent some things to showcase the point:
- If the shadow creatures cannot travel through water, animals could learn to sleep underwater (using the "upside down bucket" style air bubble - or simply by evolving waterbreathing).
- Can these creates walk through walls or are they bound by the physical realm? Because if it's the latter, any form of closed hole/house/door will keep them out.
- If the shadow creatures cannot stand even the dimmest of light, other creatures may flock to places with light: a pool of lava, a mountain of phosphorus, anywhere near bioluminescent creatures, ...
- If the shadow creatures cannot fly or jump high, animals can safely sleep in trees whose bark is covered in bioluminescent creatures.
- How do the shadow creatures track their prey? Camouflage, hiding your smell, looking like a different (to the shadow creatures inedible) animal, ... are all viable options to counter whatever method the shadow creatures rely on to hunt prey.
Remember, you don't need to perfectly counter the shadow creatures, you simply need a statistically significant population to survive between birth and procreation.
- Maybe once they've procreated, the parents leave the nest and give off a different musk, one that smells tasty to the shadow creatures, so that the parents are more likely to get eaten instead of the children, thus perpetuating the species.
In absence of any viable biological solution, instinctively fearing the dark is always possible. In other words, if an animal does not develop any biological countermeasures, maybe the instincts of the animal merely adapt so that the animal only feels safe in locations that minimize the odds of being killed by the shadow creatures.
I see a problem with luminescent animals in the night, because they'd be easy to spot for predators, even though they might repel the "Darkness."
It's a numbers game. Which kills your species the most: the shadow creatures, or other "normal" predators?
If the shadow creatures are the biggest natural enemy, then the animals will evolve to counter the shadow creatures more than the "normal" predators. If the shadow creatures only rarely kill (compared to the other predators), the animals will evolve to counter the other predators.
Evolution always favors the statistically highest survival chances.