jerk/bully, becoming nice

In most of these there isn't exactly a moment where "something happens that makes them try to be better" - it's a bit more gradual than that:

• Semantic Error
• Tempted
• Cheese in the Trap
• Boys Over Flowers
• The Smile Has Left Your Eyes
• Witch's Romance
• 100 Days My Prince
• Falling for Innocence
• Jealousy Incarnate
• Secret

Kiss Me 
Love by Chance 2: A Chance to Love 
SOTUS 
Theory of Love 
U-Prince: The Handsome Cowboy 
Devil Beside You 
Easy Fortune Happy Life 
Fall in Love With Me 
It Started with a Kiss 
Marmalade Boy 
Moon River 
The Prince Who Turns into a Frog 
The Rose 
Why Why Love 
Successful Story of a Bright Girl 
The Greatest Love 
You're Beautiful 
Hana Yori Dango