|Brave Lance Double Moonbow Catria. Kills Hardin, Homeless Tiki (Legendary Tiki), Effie without Wary Fighter, Maltet Hector, Some greens (not Surtr, but then again, that's setting the bar too high).
Ardent Sacrifice with -HP can get Catria into at least Brazen Atk/Spd, if not Desperation (75% HP depends on merges).
This way, You can control Catria's Player phase.
Alternatively, if you don't want to rely on percentages, you can use Swift Sparrow.
Moonbow is perfect for wasting basically everything (all the aforementioned characters). Galeforce is usable, but it's kind of a waste. Kill power is insane with double moonbow.
Desperation works wonders with moonbow because it guarantees double activation on a quad before the enemy even gets to counter.
Guard works well with Swift Sparrow, because there isn't a threshold problem like there is with the combination of Guard and Brazen Atk Spd.
Flier Guidance is very useful because it makes fulfilling Catria's "Triangle" refine condition much easier. Goad Fliers works for support, but the extra fliers will ensure that Catria can attack at full power.
Finally, Flier Formation works as reverse flier guidance to get Catria into potentially usable scenarios (as in situations that can activate "Triangle" reliably). It's very powerful offensively because now Catria can get in to attack without any specific movement tactics using Reposition.
Furthermore, it allows Catria to use aforementioned Reposition to position her allies well if she chooses to use it.
Suggestions for teammates: Red Sword that can kill Surtr (Palla, Caeda). Enemy phase flier (F Grima, Myrrh with Iote's shield, S! Tiki with Iote's shield, etc.), Ranged slot (Flier Mage, Eir, Kinshi Rider. I prefer GIGA NINO (Scattered Fangs Nino), but any bladetome mage works as well).