Do these take two playthroughs?

Things like Wood & Wasp, there are at least two puppet choices where one gets locked out when you choose the other, so will you need to run a second game or is it a New Game + kind of thing?

Late answer, but yes. You have to play through at least 2 times as Wood Elemental/Wasp and Falon/Darius are mutually exclusive.

Or I think you could just make a save, get one, load the save and get the other. That will 99% trigger the achievement too.