Can an unequipped Chump really lose to the Rubber Ducky?

Fun answers! (creator of the game here)

We specifically created the rubber ducky's moveset so that it was impossible to lose to them. They only turn up in that very first tutorial fight in the first quest.

A few days after release someone turned up on our forums saying the game was too hard and that they had even lost to the rubber ducky in the tutorial. We called them out saying it was impossible to lose to the ducky, when someone else posted a screenshot (see this thread) showing them dying to the duck!

We were so impressed by their ingenuity that we added an achievement for it.

Personally I did it with:

the cat burglar (they have no blocks and have two attacks that queue up damage for later turns) and no shrine, so only needed to grind 50 gold losing the tutorial quest.

There is also a third solution:

As before, grind out 100 gold with the Chump and fail the quest. Purchase the Bruiser and the Talisman of the Crone. On the Ducky's first cycle through the deck, you must play "You tryin' something" against "Uhhh...." You must play "Nice try, chump" and "Oi!" or "How do you like this?" against his other two cards. On the second cycle, as long as the Ducky plays Headbutt before Anger you can succeed.

The odds are more complex for this case so I didn't calculate them yet.

41% Chance of Death by Ducky

For completeness sake I offer a 2nd solution: (PS: I had no idea it would turn out better!)

Again, grind out 100 Gold with a Chump & fail the quest. You might as well get the "Look At The Size Of This Thing" achievement while you're at it. Purchase the Talisman of the Crone & the Hidden Den (Cat Burglar). When you face the Ducky, your 1st turn must be a 1 damage attack (Pounce or Scratch), followed by a succession of Catnip plays. Ducky will kill himself on turns 4 or 5, so you won't need more than 3 Catnips in a row. (Feel free to smack him into oblivion on that last turn!)

The smaller 6 card starting deck dramatically improves the odds that you have a good card for the 1st turn. The 4 card hand size and 2 cards that don't directly deal damage make turns 2 & 3 a guarantee. Giving you a 93% chance of keeping him alive to his reshuffle. A larger chance of failure appears on turns 4 & 5 due to the possibility of Ducky suicide (Anger) or your inability to hold off killing him (which you will do in style) because you drew your damage card when he draws "Uhh...".

18% Chance of Death by Ducky - 50 Gold Edition.

This character can die to the ducky without you spending 50 Gold on "the blessing", but you've only got a 54% chance of keeping Ducky alive until turn 4, and, as you will be killing him on turn 4, Ducky must deliver the killing blow on turn 4.