L.Eirika's A slot

Breath skills are for melee infantry and armoured only. I personally wouldn't get rid of Atk/Spd Solo.

DC on Eirika always sounds great, as long as you don't have better options, who need DC (H!Myrrh, Myrrh, maybe W!Fae, S!Tiki, Effie, Sheena... etc. )
If Eirika is your favourite character and you want her to be able to play defensive as well, I'd say go for it...
I don't really like Hrid too much, even if his debuffs are nice... give his DC to Sword Rein or a +10Ares and they do a better job as Sword Cavs

Even if you don't put DC on Eirika, i would never merge that Hrid... rather save his DC until you need it...

Cavalry/Flying units can’t abuse Steady Breath due to their movement type. Only infantry and Armors can use it.

She doesn’t have great deference’s to use DC, I think Atk/Spd Solo is great as it has synergy with her weapon.