I finally got this to work. It took a few runs and I'm not 100% sure what the issue was previously.
Per the dev:
Back to Basics checks for damage done by weapons. Things like pots, grass and creatures can be damaged by weapons, but 'interacting' with them will not damage them. Progress critical things like the crystal blockers and gongs are always interacted with, even when attacked, and will not affect the achievement.
A followup tidbit from the dev is that hitting jellyfish with your boat counts as damage and will interfere with this achievements (and Up Close and Personal and Keep Your Distance). This probably applies to sharks, too. Avoid them at all costs.
Here are the specifics of my successful run, most of which is probably irrelevant to the achievement:
I deleted all save data to start on a fresh save file.
I played in Adventurer mode and never died.
I used only the grass hull/mast and never upgraded the boat.
I crafted a fire and drying rack on the boat to cook meat and dry leather.
I ate both meat and non-meat.
I didn't craft any bags or containers.
I killed various creatures for materials.
I intended to use the knife exclusively but ended up using stick spears to kill a tremorlork for progression.
I crafted the three tools (hammer, bone knife, and axe) but not the glider as it was never needed.
I crafted a grass sling and used to to shoot a rock to progress one tower.
I never broke blue jars.
I never interacted with sea shard pillars.
I never collected blessings or interacted with blessing pillars.
I collected the first white orb at an early island bonfire to receive the parry ability and ignored the rest of these (at island bonfires and after chapter bosses).
I did not craft a spectral spear or arrows to get past a crystal blockage at a ch5 tower, instead miraculously finding a path to platform around the outside.