This achievement is much simpler than it sounds.
Since each room is randomized as you go through each of the worlds, you will have random drops. DO NOT PICK UP ANY OF THE ENEMY DROPS as doing so will immediately void the achievement for that run and you will have to start over.
This also includes any of the ritual rooms as well, as those count as blessings.
For simplicity sake, you can reduce the games speed in the settings, and play at a slow speed, making sure not to accidentally pick up any items as this game is a heavy button masher. This is what I did (set it around 30-40%) and got it on my second try.
If you mess up, just start over and try again, wont be too bad.