Legendary Byleth (F)

Weapon: Professorial Guide

Assist: Rally Up Atk+ / any 400 SP assist / Positional Assist / flexible

Special: Ruptured Sky

IVs: +Atk or +Spd / -HP or -Def or -Res

Passive A: Atk/Spd Ideal 4 / Atk/Spd Boosting A Skill / flexible

Passive B: Windsweep / Watersweep / Lull Spd/Res / flexible

Passive C: Goddess Bearer

Sacred Seal: Blade Session / flexible

• This build aims to emphasize Byleth’s Atk and Spd to deal high damage on player phase, with the option of running skills to boost Arena score if she’s used in a mode where that matters (Arena, Arena Assault, Mjolnir Strike, Allegiance Battles, etc.)
• The A skill and seal should boost Atk and Spd. Atk/Spd Ideal is generally the best choice of A, as it provides a guaranteed buff of +7 Atk and Spd as long as the buff from Goddess Bearer is active, and an additional +2 if Byleth is at full HP, which is often easy to maintain if using Windsweep or Watersweep. Blade Session is generally the best seal as it provides up to a +9 boost to Atk and Spd, but other seals like Atk/Spd Solo or Life and Death also work well.
• If Byleth is used on an arena team, the ideal Assist is any that costs 400 SP, which includes all double Rally+ skills, all Rally Up + skills, Harsh Command+, and so on. The particular choice of rally is not particularly important beyond the scoring. If used in other modes, a positional assist like Reposition is generally the most useful. 
• Ruptured Sky is the best Special for use in Arena or modes with similar scoring, as it costs 500 SP, the same as other Specials like Blue Flame or Aether, but has a lower cooldown that allows Byleth to activate it on the second attack in any combat she can follow-up attack due to the anti-Guard effect of Professorial Guide. It is also a reliable option for damage in other modes, though there are particular cases where another option like Moonbow would be better, or Luna in conjunct with Flashing Blade seal. 
• The ideal boon is +Atk or +Spd to boost Byleth’s damage and allow her to more consistently follow-up attack. Any of her other three stats are a good choice of bane. 
• Windsweep and Watersweep are both good options for B skill. Windsweep allows her to avoid counterattacks from physical units if she outspeeds them, while Watersweep does the same for magical units. The follow-up denying conditions of these skills are negated by the Null Follow-Up effect from Goddess Bearer. Windsweep is more generally useful across modes, as physical units are generally more common, particularly among those with Distant Counter. However, there are a decent number of dragons and mages that are relevant as well, particularly if using Byleth in Arena in Wind season; Watersweep allows her to avoid counterattacks from both Legendary Corrin and Legendary Micaiah, allowing Byleth to potentially KO them while taking no damage. Her base Lull Spd/Res is also a decent option that improves Byleth’s damage and ability to follow-up attack by reducing enemy Spd and Res and negating buffs in those stats. 
• Goddess Bearer is a fantastic C skill that provides Byleth a +7 buff to Atk and Spd, a teleportation effect in the style of Ground Orders, and Null Follow-Up so long as she starts her turn within 2 spaces of an ally. It also costs 300 SP, so it is ideal for scoring. There is generally no reason to replace it with another skill for this type of build. 

Weapon: Professorial Guide

Assist: Rally Up Atk+ / any 400 SP assist / Positional Assist / flexible

Special: Ruptured Sky

IVs: +Atk or +Spd / -HP or -Def or -Res

Passive A: Atk/Spd Ideal 4 / Atk/Spd Boosting A Skill / flexible

Passive B: Windsweep / Watersweep / Lull Spd/Res / flexible

Passive C: Goddess Bearer / Joint Dist. Guard / flexible

Sacred Seal: Distant Guard / flexible

• This build attempts to capitalize on Byleth’s unique support capabilities from Professorial Guide while maintaining some offensive capabilities. 
• The choice of Assist depends on the mode: for Arena, a 400 SP assist is ideal for scoring. For modes where SP cost is not a concern, such as Aether Raids or Summoner Duels, a Positional Assist is often the most useful choice. 
• The B skill could be substituted for something like Chill Atk to provide a debuff to a single foe, but the usefulness of this is debatable compared to Byleth’s own combat potential and ability to avoid counterattacks from either physical units with Windsweep or magical units with Watersweep. This can allow her to deal with single annoying units the team might otherwise struggle with, such as Fallen Edelgard when using Windsweep. 
• The C skill is flexible. Goddess Bearer is a fantastic skill for Byleth’s own combat, but does nothing to help out her allies, so it can optionally be swapped out for something like Joint Dist. Guard or Joint Drive Atk to provide allies within 2 spaces a slight stat boost in combat, or something like Infantry Breath or Infantry Flash for a Special-charge effect specific to Infantry allies. Inf. Hexblade is another decent option that allows adjacent infantry allies wielding a physical weapon to target the lower of the foe’s Def or Res while also boosting their Atk and Spd by 2 in combat.
• Likewise, the seal can be used to support allies, with Distant Guard being a generally useful option, with many other good choices like Close Guard or Drive Atk.