18% Chance of Death by Ducky
You are correct in thinking that the Chump cannot lose this fight.
It takes the Rubber Ducky 3 turns to cycle through its deck. In those 3 turns, it will deal 3 damage to you and 2 damage to itself. In the meantime, you also have to play 3 cards.
If you play "Cower" twice and "Eyes Closed Punch" once, you will deal one damage to the Ducky and block 1 (or 2) damage to yourself, leaving you with at least 3 health and the Ducky with 1. There is no card the Ducky can play on turn 4 that can hurt you enough to kill you.
If you play any other card combination on the first 3 cards, you will have done at least 2 damage and the duck will be dead by the end of turn 3.
To complete this achievement you need to use a different dungeoneer and purchase one of the blessing items (spoilers at bottom). In order to do this, grind your way up to 100 gold through map exploration and treasure, then lose a fight or quit the dungeon, and make your purchase. When you re-enter the dungeon, you will start the stage over, and therefore will have a chance to fight the Ducky again.
Even after this, there is some luck involved; you may have to retry the fight a few times since the duck has less than a 20% chance to win.
You must purchase the Apprentice and the Talisman of the Crone. The Apprentice has a 7-card starting deck but also the card "Intuition" which draws two cards but does not attack or block. Spam this ability at every opportunity. On your first two turns, play intuition and a 1-damage spell. You will have drawn your entire deck at this point (4 card starting hand + 1 card drawn on turn 2 + 2 cards drawn from Intuition). If you draw Intuition again on turn 3, continue to cast it until you lose.