To get this Achievement, you must beat the final boss after collecting all 36 Heart Squids without ever turning them into Hearts at the Squidsmith.
-That means you will have only your starting 3 Hearts for that fight.
(I recommend you NOT try to combine this with a Speedrun save but that's up to you.)
Each of the 5 Labyrinths (not #6, for the Final Boss) has 3 Heart Squids each. They can always be collected in one run of that area, sometimes requiring a new ability unlocked in that area.