There are an absolute ton of side quests in Hogwarts Legacy. Some involve helping people, some involve rescuing beasts, while others involve expanding the capabilities of the Room of Requirement, when you finally get around to unlocking that. These side quests often unlock throughout the story, while some of the open-world quests are unlocked as soon as you get full, unfettered access to the open-world.

Side quests in the game are indicated by a small black and white icon with a location marker when looking at the map itself. While some are given to you automatically and via the Owl message service, others you’ll have to come across yourself.

They’re all super easy to find though, mainly because: a.) the ones in the open-world pop up as soon as you enter the village they’re in; and b.) the ones in Hogwarts (look out for the black flags in the map screen, that means there’s a quest there) and Hogsmeade show up in the map screen if you zoom out far enough and hover over each place. 

Simply finish all 57 side quests and this achievement will unlock. Here's a full list of Hogwarts Legacy side quests, which includes assignments, relationship quests and main quests too, including when they all unlock.