This one is pretty straight forward. Just do kill two contract related monsters without using any of the mentioned items.
An easy way to do this is to start a new game on "Just a story" and skip all the dialogue. As soon as you get to "White orchard" do the "Devil by the Well" contract from the notice board, you can pretty much just button mash (using
) for an auto win.
Next continue with the story until you have to kill the gryphon. Killing the Gryphon will net you the trophy.
Of course you can do this mid playthrough, just remember to unequip your mutagens.