Soo.. know your enemy - Rubber Ducky have Irratable II and stupidity I, so it have one Uhh.. (nothing) card, one Anger (1 dmg, -1 hp) and one headbut (2 dmg, -1 hp) card. that way it becomes really hard to die by the hands.. err.. wings.. of rubber ducky, becouse of -1hp of it's own attacks. Problem here is that you have 5 hearts while ducky have 4.

You'll need to deal no more than one dmg to ducky so he could kill you while killing itself with LUCKilly drawn headbutt, also no physical defense (except against uhh card). Question is HOW the hell you can do it?

Answer - Apprentice with Crone's talisman.

Why apprentice - becouse he have one totally not attacking card - intuition wich also gives you +2 cards to hand.
To die the way i found (maybe there are some other ways) you'll need some grind - you'll need 50 for apprentice and 50 for kron's talisman. You could make money by killing ducky, than killing one more monster and abbandoning dungeon (collecting coins if you lucky to get them). Remember not to win the dungeon as you can't replay that mission on current build (afaik).

When you'll get mentioned upgrades start the dungeon with apprentice and hope for 'lucky' cards - you need to get intuition at first or second time to have chances to die.

i'll just make an example of fight: (it's not hard to catch a strategy from it)
1) you 5 hp, ducky 4hp
you have 4 (of 7) cards in hand (by crone's talisman)
ducky played headbutt (2 dmg, -1 hp)
you played intuition (2 cards)

2) you 3 hp, ducky 3 hp
you have 6 (of 7) cards in hand, intuition in discard pile
ducky played anger (1 dmg, -1 hp)
you played sparks (1 dmg)

3) you 2 hp, ducky 1 hp
you have 6 (of 7) cards in hand, intuition in hand
ducky played Uhh.. (nothing)
you played intuition (2 cards)

4) you 2 hp, ducky 1 hp
you have all 7 cards in hand
ducky played headbutt (2 dmg, -1 hp)
you played intuition (2 cards) - actualy don't matter, just dont play quick cards.

5) you 0 hp, ducky 0 hp
PROFIT=) - your achievement packed with another one - NOOOOooooo (if you didn't get it already)

Here "4)" can be delayed by Uhh card (you still playing intuition in that case). But if ducky will play anger (1 dmg, -1 hp) you'll still win with 1 hp left and get another achievement, if you still played intuition - Pacifist (if you didn't get it already)