So I just finished ToCS3 and started a nightmare run which I'm going to use to get character notes and tresure chests I missed. I did manage to get the achievement for finishing every quest in the game in my first run though, is there any reason I should bother with them again instead of blasting through the game?

If you're only missing School Directory, Chest Quest and Conqueror of Nightmares, then sure, you don't have to redo all of the quests again.

Yeah thought so, just wanted to be really sure. Thanks!

No problem. Since you look like CS3 is your first Trails game, I'll give you a piece of advice along the way. Don't play CS4 without at least experiencing all the earlier games first, not just CS1+2 but also all the Sky and Crossbell games.