The story was about Albus turning into a mischievous boy, who bullied Scorpius at school.
As he was Harry Potter's son, everyone doted on him and let him bully Scorpius for revenge.
Neville Longbottom was a Herbology teacher and he let Albus get away with everything.
One day Albus went to Forbidden Forest with Scorpius and Hagrid as a punishment for something I don't remember. Hagrid let the two of them together so Albus could bully Scorpius. Albus did something stupid and got attack by a werewolf/beast/monster (can't remember). Scorpius saved him. They became best friends.
Harry and Ron didn't like this. Igor Karkaroff appeared with a certain evil plan. He created a tournament. Albus and Scorpius knew about his plan and they participated the tournament together. They won the tournament and defeated Igor together.
I think this story was published between 2008-2009, after the last Harry Potter book came out. It was a long fanfic and there was only friendship between Albus and Scorpius, no love.