Aleron fought against many monsters, though he killed all of them with one-shot attacks.
However, he still exercised his magic and physical body to the fullest in his way to consolidate his foundation.
Once he finished with that, Aleron relaxed and just waited for his Legendary Awakening, which would eventually come to him as he believed.
For other people, they had to trigger their Legendary Awakening by establishing a Legend of themselves within their mind, which would then take shape into some form of power. People usually triggered their Legendary Awakening by achieving a notable feat.
But it was basically the synthesis of one's desire, ambition, wish, or whatever like that which they firmly came to believe they would fulfill.
Leaving the forest, the Roxen continued the carriage for three hours before the group finally arrived at a major city.