Boukensha ni Naritai to Miyako ni Deteitta Musume ga S Rank ni Natteta

Retired adventurer Belgrieve thought he was done with excitement...but his peaceful life is upended when he discovers a baby abandoned in the nearby woods. As her adoptive father, he teaches his new daughter Angeline everything he knows about the adventuring life—a past he had thought long forgotten after he lost his leg in battle.
Angeline idolizes her father and wants to follow in his footsteps, so she leaves home for the big city. As the years pass, she ascends the ranks, eventually becoming renowned as an S-Rank adventurer: the Black-Haired Valkyrie. But it turns out that being the best comes with its own struggles, and she can barely catch her breath between battling fiends. With everyone turning to her for rescue, can Ange get out ahead of each new disaster and finally reunite with her beloved dad?

(Source: J-Novel Club)