Sounds like The Lazy Lord Masters the Sword.
From Baka-Updates:
After witnessing the shocking death of his mother, young Airen Farreira uses sleep to escape his painful reality, earning him the nickname, “the lazy lord”. Yet, in spite of others’ jeers and whispers, Airen has no intention of changing his ways. But when he awakens one day from a dream about a mysterious swordsman, his life’s trajectory takes a complete turn...
The story begins with a villager writing in his diary about a mysterious man who settled in his village and religiously practiced sword fighting every day for 37 years, until he collapsed and died. Then a teenage boy wakes up in bed, having just dreamed all that.
The boy, Airen Farreira, is the firstborn son of a baron, but is nicknamed the 'lazy lord', as he's done nothing but sleep all day since losing his biological mother at an early age. He now has a kind stepmother, and an ill-tempered stepsister, named Kiril, who's also a sorcerer.
After his dream, Airen can't get back to sleep and feels restless, his body craving action. He decides to take up swordsmanship, and heads to his family's training hall to practice, picking a huge sword off the wall, just like the one he saw the man in his dream wielding.
He practices alone for the next two weeks, and finds it gruelling, as his body isn't used to this sort of exertion, but presses on regardless. An elderly knight looking on is impressed by his determination, and recommends him to a prestigious swordsmanship academy.
The top student at the academy is an aloof, noble girl named Illia, and the second and third best are a tomboyish, common girl named Judith, and a cocky, noble boy named Brett.
The first few months of training are focused on exercise rather than swordsmanship. Airen is much weaker than the other students, but trains hard, and Illia advises him on how to lift weights correctly. Over time, his fitness improves dramatically.
After four months, the students begin swordsmanship training with wooden swords. Airen is ranked the lowest of all the students, but gradually works his way up, with Judith assisting as a practice partner.
After 12 months, the students undergo their final evaluation, in which they're to be judged on their potential. Airen states his intention to demonstrate his potential with a vertical slash, to the bemusement of the other students.
To everyone's shock though, Airen performs a vertical slash so powerful that it opens up a huge rift in the ground in front of him.
Later in the story, Airen meets a talking cat sorcerer, named Lulu, who offers to take Airen on as his student, and sends him into a mystical dream-state, enabling him to explore his own heart.
