I made a video below for this. I've encountered her a few times now and I think I can help with this. Here are the details:
How to Trigger: Once you begin Chapter 3, any time you start a battle you have a random chance to spawn the Valkyria. There's no rhyme or reason to this. I did battles in Avalune countless times and only once did she spawn. She's also spawned on other missions. You'll know if she can spawn because you'll hear it in briefing and because there will be a time of day counter in the upper left corner.
How to Know She's There: The Valkyria spawns as soon as the timer hits the moon (the circle). But a minute or two before that, you'll know because the game music will end and be replaced by a sad Valkyria song. It's much different so you're sure to recognize it. If it's very close to dark and you hear the same old tune, she's not spawning.
This does mean you may need to go battle after battle hoping she'll spawn. It sucks. But she will spawn. I've seen her four times in about 30 battles.
Difficulty:
If you want to get this quickly, play on easy.If you're playing on Easy, you need to be the same level as her probably, though it may be doable with less. If you're on Normal, you'll need to be 10 levels above her. You can change this in the options menu when you're in town. Difficulty doesn't affect trophies so it's safe. She does immense damage on Normal difficulty.
Her level is determined by the level of the mission, which in turn is determined by your Chapter. You can see the level of the battle on the world map.
Strategy: There's not much you can do other than zerging her with the right elements. She has an orb surrounding her. You need to use Ragnite of the opposite color:
Red vs. Blue
Green vs. Yellow
Spam it on her and it will do more and more damage. Once it evens out, start nuking her with whatever you have. If you have the Bravery spell, which boosts your attack damage, use it. Otherwise just keep going and resurrect your allies as soon as they go down (which they will on Normal for sure). Ophelia's healing song can be a lifesaver on Normal.