Played two different game slots simultaneously to confirm the relevant actions: one that I always reset to the previous savestate when encountering the "Small Donkey" achievement - in the other one I accumulated all my previously found mistakes.
Following, the relevant actions ordered by occurrence:
*** Spoiler - click to reveal ***
# Achievement Requirements: Large Donkey
## Case 1: Andouver
> location: MRS. ASCHER'S BEDROOM
> dialogue with Mary Drower
> → 🏆 Large Donkey [1/8 ✔]: make her cry by suggesting divorce
## Interlude: Whitehaven, Part I
> location: JAPP'S OFFICE
> dialogue with Japp
> → 🏆 Large Donkey [2/8 ✔]: claim the murderer is unpredictable
## Case 3: Churston
> location: CLIFFSIDE
> dialogue with Japp
> → 🏆 Large Donkey [3/8 ✔]: claim the murderer is opportunist & theft might have been the motive
> location: MANSION LOUNGE
> dialogue with Thora Grey
> → 🏆 Large Donkey [4/8 ✔]
> Ask for her version of the facts.
> Ask the reasons for her aversion to Franklin.
## Interlude: Whitehaven, Part III
> location: POIROT'S APARTMENT
> dialogue with guests
> → 🏆 Large Donkey [5/8 ✔]
> Tell Megan not to be in such a hurry.
> → 🏆 Large Donkey [6/8 ✔]
> Agree that the subject creates a feeling of discomfort.
## Interlude: Whitehaven, Part IV
> location: POIROT'S APARTMENT
> call hotel owner (requires to tell Japp that Poirot will take care of informing Donbar)
> → 🏆 Large Donkey [7/8 ✔] (prevents 🏆 Sheriff Moustache)
> Ask to speak to Donbar.
> Say that he's a killer.
> Warn him that Cust is dangerous.
## Case Closure: London
> location: POIROT'S APARTMENT
> investigate cupboard with gun
> → 🏆 Large Donkey [8/8 ✔]: use real bullets and give the revolver to Hastings