I did this on the Thief's Elimination Episode in a fight against the Drain Monster on Floor 3 (who takes 1/2 damage from poison due to resistance).
I had the skills:
Poison Slingshot - 12 to inflict 4 Poison
Poison Needle+ - (Max 2) Inflict 1 Poison this turn (5 Uses this turn)
Lockpick - Split a dice in 2
Duplicate - Duplicate a dice
Bandage - (Odd) Heal 1 (just to burn the occasional dice/keep me in the fight)
And the stolen poison skill from the Drain Monster
As the Drain Monster is resistant to Poison, it allowed the match to go multiple rounds whilst I kept duplicating/splitting my 1's, especially if you have Unlucky Roll (Thief's Special skill) ready. And slowly just stacked up that poison to 30. On the last round my poison had stacked for 33 (hitting the drain monster for 17) even though he had just 5 health left I got the achievement.