Just managed to re-capture Lumine day 20 on hard mode. Basic strategy:
Day 1; use careful positioning so you can swarm her and take her down without any losses, quite easy to do if you stay just outside her attack range. Make sure to start crafting a Dark Wedge at the alter.
Day 2; Make 4 new Hilichurl teams, use your 4 existing units to attack Falcon Coast, then swap out teams as needed so you have 6 full teams in Falcon Coast.
Day 3; Fischl spawns in, and should move to Thousand Winds Temple. I've also seen her not move, or move to Forgotten Sword Cemetery. It's doable to get her in a sweep, but it's better to attack her so your units are grouped together. In any case, with careful positioning and a little luck it's actually possible to surround and capture her before she can get off her elemental burst. Kind of worth restarting the battle if you don't manage to do so, as it'll save a lot of casualties. After catching her, immediately start corrupting her at the alter. It's very expensive, but you should be able to finish before day 12. Which means you can start breeding her for Nycto Hilichurl, and should be able to get 6+ of them by day 20. Finally, Evacuate your forces from Thousand Winds Temple and Forgotten Sword Cemetary. With the amount of threat you just generated, both locations will likely fall under attack, and you won't be able to defend them with your limited forces.
And that's the basic strategy. Some additional points;
If you capture any vision wielders besides Fischl, before you corrupt her, you won't have enough Abyss Power to finish the process on time. As such, you'll need to capture Windrise and destroy the nearby goddess statue for the bonus Abyss Power in order to finish on time. If this happens, you'll want to evacuate Windrise immedately afterwards. Knights are very tough to fight with just basic Hilichurls, and with how much threat destroying a statue generates, one will likely spawn immedately to retake Windrise. And with your forces likely depleated after taking the camp? That's not a wining battle. Evacuating will let you replenish your forces and retake the province next week, while decreasing your threat below the knight threashold in the meantime.
Amber will probably appear fairly quickly, likely on week 5. This is a fairly aggressive strategy, and we'll probably reach her threashold for spawning after retaking the Forgotten Sword Cemetary on week 4 after Anna comes to play after week 3 (which is why we evacuated). She's a fairly simple fight all things considered. She's a fairly simple fight all things considered, as she's a solo fighter. So just avoid the bombs, avoid clumping too many teams together so she can get 3 at the same time with one bomb, and she'll go down easy. Collei, on the other hand, is a much more puzzling challange. It's actually possible to beat her with just 4 standard Hilichurls, but it requires very careful posiitioning to actually do so. See, if you can get her to end her second turn next to one Hilichurl, and within the range of 3 others, you have enough damage output between all 4 to switch her AI to retreating, instead of using her elemental burst to kill all your units. But in order to set that up, we need to exploit the AI a bit. Namely; the AI prioritizes hitting as many units as possible instead of dealing lots of damage to a single unit, and tries to target the furthest unit possible. And her main attack is an AOE that deals a lot of damage to the center, but not much to the outside edges. So, you'll want to line up 3 hilichurls in a verticle line with one space in between, then one two rows back from the others, forming a triangle with 2 of the front row hilichurls. Do it right, and close enough to her attack range, and she'll move right next to the middle Hilichurl so she can hit the one in the back with her basic attack. The perfect position to hit her with 5 regular attacks, and 4 squad captures. If you don't do this and force her to retreat, then you'd be dealing with her elemental burst - which is a bit of a menace. Zone of Damage effect that hits all teams within the field, whenever a team ends thier turn in the field. two hits are enough to kill a basic Hilichurl team, and one hit will be delivered when setting up. It's a really OP menace in the early game if you don't bring ranged units.
As for the Lumine fight itself, 6 Nycto Hilichurls are the minimumn requirments. But you don't necessarially need them at full strength. I was able to do it with just 5 full strenght, and one with 3 Hilichurls in support. The more improtant aspect is being able to consistantly hit her with 4-5 Nycto arrows between her movements. Enough to re-apply the Nycto status condition on her. Which should prevent her from just wiping the field. Which is easy enough if you just bunch all your teams together in a tight 2x3 formation.
