During the battle against Yahaba and Susamaru, Tanjiro claims he breaks his leg after chaining his strikes together. Following the fight, Tanjiro stands up and walks away injury free. How did Tanjiro heal his broken leg?
Tanjiro was able to heal his broken leg through a plot hole or a misidentification on his part. Either the mangaka forgot that Tanjiro’s leg was broken, or the character believes it is, but realizes later it’s not.
Nobody in the story has any healing abilities by this point. Tanjiro is unaware how to use breathing techniques to heal himself, and Nezuko lacks her Blood Demon Art abilities.
Tanjiro believes he has a broken leg
In chapter #18, Tanjiro defends himself against Yahaba, a powerful demon. The enemy is capable of launching arrow-shaped projectiles at incredible speeds and angles. Things begin to seem desperate.
As a last resort, Tanjiro commits to using a technique chain. This will allow him to utilize multiple water-techniques in quick succession, but he’s inexperienced on the subject.
Tanjiro has never done back to back techniques such as this. He says it feels as though his “arms are tearing off,” and he doubts he can keep up with the techniques. He uses his water powers. Waterfall Basin, Striking Tide, Water Wheel, and Whirlpool are all utilized before Tanjiro collapses on the ground in exhaustion.
He wheezes on the ground in pain. “B-broke my ribs,” Tanjiro says. “And leg…” Tanjiro is far too-tired to swing his sword, and clutches it within his teeth.
He stands up and walks away, injury free
The following chapter, Lady Tamayo is able to defeat the pair of demons. Tamayo claims she can help Nezuko with the defeated demon’s blood, and Tanjiro reflects over the battle.
Tanjiro, who claims to have a broken leg, then stands up and walks to a staircase. He heads underground and runs towards Nezuko, hugging his sister.
It is not directly explained how Tanjiro was able to heal his leg this fast. Later in the series, he learns a breathing technique that allows him to heal body injuries. Yet, he is not taught this yet. It can be chalked up to either a plot error or a misread on Tanjiro’s part.
There appear to be two distinct possibilities. The mangaka forgot that they identified Tanjiro as having a broken leg. Or, Tanjiro himself incorrectly assumes that he breaks his leg.
Tanjiro’s leg doesn’t heal for any particularly magical reason.
So that’s the answer. Tanjiro was able to heal his broken leg through an error by the mangaka or a misidentification by Tanjiro.