>>536578421
They're all so different in game terms.
Aegir: Gear lab, so keep farming Operation Siren for the Iron Blood 305mm SK C (AP ammo) or Sakura 310mm Type 0 (HE ammo).

von Hutten: She's usually run with HE guns because she's so much better at mobbing than bossing. The rainbow triple 406mm Mk7 is best (Gear Lab if you didn't get it some other way), but the purple 406mm Mk6 isn't bad.

Prinz Heinrich and sisters: the rainbow CA guns are best, but those are hard to get. The purple 283mm is good when the enemies have shields. It's in purple and gold Iron Blood tech boxes. If shields aren't present, you're probably better off with the gold twin 203mm SK C (the one that's dark blue on top) from Iron Blood tech boxes, 7-3, and 8-4.