After about 100 tries on all characters, I got the achievement with the Watcher. I also got the "You Are Nothing" achievement in the same run as I got an infinite combo going and beat the final boss first turn.
Study the infinite combos:
https://slay-the-spire.fandom.com/wiki/Infinite_Combo Before starting: pick any character as they all have infinite combos, pick a good blessing from Neow. I like the ones that remove cards. Stay away from blessings that add more cards to your deck, including curses.
Go for the path with most question marks, least elites, and most shops. Prioritize in that order. You are praying for card removal events in the question mark rooms. Also remember that shop is guaranteed removal as long as you have the money. As such, you should always purchase card removal from the shopkeeper. If you get a relic like Smiling Mask that makes shop removals always 50g, then go for most shops obviously.
Your goal is to find cards to make an infinite combo, while removing your starting cards. I like to skip taking cards most of chapter 1, then starting to add any infinite combo cards I can find in chapter 2. Still, you'll probably only want to add 1-3 cards to your deck the entire run.
With the guide out of the way, here's what my build looked like. Remember that this is just how I got the achievement:
Relics:
Pure Water, Smiling Mask, Nunchaku, Empty Cage, Girya, Runic Pyramid, Cloak Clasp, Question Card, Red Mask
Cards:
Eruption+
Vigilance+
Signature Move+
Rushdown
Inner Peace+
My infinite combo was playing Rushdown followed by Inner Peace (1) to go into calm, then Eruption (1) to go into wrath, giving me back the 2 energy and cards (with Rushdown), allowing me to do it all over again with Inner Peace and Eruption. Signature Move helped me tons, I got it in the middle of chapter 2 and it allowed me to deal 80 damage with one card. As you can see I got Smiling Mask and Empty Cage, two really good relics for this achievement.