There are three sets of achievements that are mutually exclusive within a single run:
The Neglect and Rivalry achievements require making mutually exclusive choices when interacting with Zote, and the Dark Romance achievement can only be obtained after achieving the Rivalry achievement.
The Purity and Happy Couple achievements require making mutually exclusive choices with the Nailmaster.
The Ritual and Banishment achievements require making mutually exclusive choices in the Grimm Troupe storyline.
The ending achievements are not mutually exclusive; you can obtain all of them in one save file. Once you complete one ending, you can re-enter the same save file at the last bench you rested at.
More generally looking at achievements that can't all be obtained in your first run, the Steel Soul and Steel Heart achievements can only be unlocked in Steel Soul mode, which is unlocked by completing the game once. It is also highly unlikely that you would be able to complete the speedrun achievements your first playthrough, especially if you are playing the game blind.