Arete

Weapon: Unity Blooms+ (+Res) / Rauðrrabbit+ (+Res) / Rauðrserpent+ 

Assist: Positional Assist

Special: Iceberg / Noontime 

Passive A: Mirror Stance 3 / Atk/Res Push 4 / Atk/Res Solo / Unity / Bond

Passive B: Lull Atk/Res / Quick Riposte / A/R Far Trace

Passive C: Joint Drive Atk / Joint Drive Res / Atk/Res Menace / Atk Smoke

Sacred Seal: Mirror Stance / Mystic Boost / Quick Riposte

• With a nice Attack and Resistance stat spread as well as a few handy tools exclusive to cavalry and red tomes, Arete can fashion up a build focused on hard checking tome units while hitting quite hard on the side. The former queen of Nohr is pretty much stealing Summer Mercedes's entire wardrobe at this point, but she does it well anyway. 
• For weapons, Arete will primarily want those that increase her tankability in enemy phase, preferably also increasing her offense. Those include:
  • Unity Blooms will be the best choice for this build bar no other rivals — unlike Rauðrrabbit, its in-combat stat debuffs are constant as long as Arete is near an ally, which should be pretty easy to do given her great movement options. Its debuffs also work in both phases, should you need Arete to do some cleaning up in player phase.
  • Given how rare Blooms is and how mind-numbingly inefficient foddering Valentines Henriette for anything other than her Far Save skill is, however, you can stick with Rauðrrabbit for a similar performance as long as you limit her fights to just one each phase — this isn't terribly difficult to do in non-Aether Raids settings. 
  • For more alternatives,  Rauðrserpent sacrifices damage output and healing for more defensive consistency on enemy phase.
• Many great Atk/Res-boosting A-slot skills are at Arete's disposal. 
  • You can opt to complete her default Push skill to 4, and the recoil suffered after combat is pretty much made up by the healing effects of Unity Blooms and Rauðrrabbit. The next best alternative is Mirror Stance 3, which comes with a Guard effect and allows Arete to stall out a lot of magic enemies out of their Special. Other similar Atk/Res Skills are up to your barracks and discretion. 
• Lull Atk/Res is this build's best B-slot option as it breaks through any potential Atk/Res buffs the enemy may have on them and simply makes Arete more difficult to break through on the magical side of things. A/R Far Trace similarly debuffs the enemy but trades the bonus negation for useful hit and run tactics. Finally, Quick Riposte is the more accessible alternative to grant Arete follow-up attacks in enemy phase, making up for her slower Speed and giving her more killing power in two hits.
• Arete's C-slot isn't terribly essential, but the listed options serve to increase her bulk, power, or both if you care to provide them. Joint Drive Atk or Res does the job easily while encouraging Arete to maintain Unity Bloom and Atk/Res Unity conditions, while Atk/Res Menace grants a bit of automated self-sufficiency in the stats swing department. Atk Smoke works well on a budget and can debuff an entire closely-knit group of enemies, but requires Arete to fight first.
• Finally, Arete can top off her performance with the right Sacred Seal. 
  • Mirror Stance (and Atk/Res Solo whenever that becomes a Seal in the future) further stacks on Arete's highly invested stats and makes her more difficult to take down. 
  • Quick Riposte is an option for the reasons stated above and if you're handling another B-slot skill. 
  • Mystic Boost provides adaptive damage negation, allowing Arete to match up even better against Dragon and Wrathful effect healers while benefitting from some nice after-combat healing. This effectively keeps Arete nice and healthy when utilized along with the healing effect of Unity Blooms or Rauðrrabbit.

Weapon: Rauðrblade 

Assist: Positional Assist

Special: Glimmer 

Passive A: Death Blow / Atk/Res Push 4 

Passive B: A/R Far Trace / Lull Atk/Res / Link skills 

Passive C: Res Smoke / Rouse Atk/Res / Flexible

Sacred Seal: Death Blow / Blade Session / Atk/Spd Solo

• If all else fails? Good old Rauðrblade's got your back. That is, as long as you have a solid plan on granting Arete all the bonuses she needs (as the tome requires visible bonuses all-around to reach a good amount of full single-shot power) while avoiding enemies with pesky bonus-negation skills like the Lull line.
• B-slot aside, the concept of bladetome makes the build rather simple. To increase the likeliness of one-shot kills, run high Attack modifiers like Death Blow in Arete's A-slot and Sacred Seal, and anything you prefer in the C-slot to help her get there — Res Smoke works better when hitting and running in Aether Raids Offense, whereas Rouse Atk/Res grants two self-earned bonuses to power up Rauðrblade as long as Arete is away from allies. 
• Due to Arete's delayed Special charge from running Rauðrblade, there's very little Specials to consider other than Glimmer, which effectively runs at a still-manageable 3 CD while providing a great potential boost thanks to Rauðrblade's great single-shot damage. 
• Arete unfortunately is a bit too slow for a classic Desperation build; Rauðrblade cannot be Speed refined and the build is generally more oriented to damage than follow-up attacking. Great B-slot choices, then, are as follows:
  • A/R Far Trace further bolsters the power of Arete's hits while softening anything she must take in return. Additionally, the Canto effect of the skill allows her to make use of her remaining spaces to escape from enemy range and towards the safely of your allies. 
  • Lull Atk/Res is an almost equally good equivalent, still featuring the -3 Atk/Res debuff on the enemy while also cancelling out any visible bonuses they might have.
  • On the more budget side of things, you can jointly provide additional stat bonuses to Arete and her ally with a Link skill of your choice. Running both a Rouse and filling missing bonuses with Link is a notable venture; a cheaply inherited example of this would be running Atk/Res Rouse (from Spring Saleh) with Spd/Def Link (Norne).

Weapon: Rauðrfox+ (+Spd)

Assist: Positional Assist

Special: Glimmer / Moonbow / Ruptured Sky

Passive A: Swift Sparrow / Atk/Spd Catch / Atk/Spd Solo / Fury 4 / Atk/Spd Push 

Passive B: S/R Far Trace / Lull Spd/Res / Lull Atk/Spd / Desperation

Passive C: Joint Drive Spd / Joint Drive Atk / Atk/Spd Menace / Flexible

Sacred Seal: Atk/Spd Solo / Blade Session / Swift Sparrow

• Yep, you read this build right. If you can grant max merges and Dragon flowers and conveniently ignore the existence of mage Eirika and Valentines Lif, this can earn you t̶h̶e̶ ̶m̶a̶x̶i̶m̶u̶m̶ ̶n̶u̶m̶b̶e̶r̶ ̶o̶f̶ ̶u̶p̶v̶o̶t̶e̶s̶ ̶o̶n̶ ̶R̶e̶d̶d̶i̶t̶!̶ ̶! a relatively credible player phase threat. 
• Rauðrfox fulfills the very purpose of the build by increasing Arete's offenses and defenses all-around by 4 effectively. It efficiently serves the build as it is easy to access and its Speed swing is the highest offered among other inheritable red tomes. Generally dealing more damage and taking less in return doesn't hurt either.
• Due to their low cooldown values of 2, Glimmer and Moonbow (or Ruptured Sky if you want to hit Dragons and Beasts harder or inflate the ridiculous inheritance value of this build even more) are preferred. These Specials are likely to activate within a single turn thanks to Arete's increased follow-up potential. 
• Of course, you'll want a high-grade Atk/Spd A-slot skill (and their Sacred Seal equivalents if available) for a speedy offense kit like this.
  • Swift Sparrow is obvious given its no-nonsense initiation condition.
  • Though Atk/Spd Catch and Atk/Spd Solo are also great recommendations with slight stat and condition differences. Catch notably offers a potentially higher +9 to Arete's Atk and Spd if her enemy is at full HP and has an existing penalty. 
  • Fury is also notable as it doubly increases Arete's bulk along with the Def/Res debuff from Rauðrfox. The recoil suffered after combat may be a turnoff, though, unless you are running the Brazen Atk/Spd Seal.
• Arete's B slot is reserved for a variety of in-combat debuffing skills fortunately available to her cavalry class. S/R Far Trace or its Lull equivalent do well in pushing the Speed comparison in Arete's favor even further while increasing her damage. Lull Atk/Spd is also considerable if some survivability is in your plan. Finally, lacking those altogether with just a budget, Desperation does a nice job of increasing survivability by enabling HP-dependent consecutive follow-up attacks. 
• Atk/Spd Menace grants some support utility and self-sufficient buffing in one package. Given how rare this is though and other C-slot skills not quite being nearly as essential aside from some Joint Drives, however, you should worry about this skill slot less than others.