You might have to disable cloud saves for this to work. Backup your own systemdata file, then replace it with the one inside the folders. There is an assumption here - that you can't load a save for which you have not unlocked an episode for so be careful. The full list of achievements which can be obtained are shown below. Unless otherwise stated, the number on the left indicates the slot to load. Some special notes for certain achievements:

Smells like Oldbag: DeMasque's Hideout comes before Security Office. I am unsure if the game needs you to check the items all in one save file, otherwise you can click on the corresponding items from the security office.

Lunchbox Specialist: Same for this achievement. Slots 6 to 9 contain the junctures to prior to the start of a conversation with Angela Starr. This one might be doable in separate playthroughs, so you can try to load the corresponding slot to if you know what you're missing.

Jean's Foreign Language Course: Same for this achievement, but this one might require one single playthrough. If so, load slot 8 which begins from the start of the part 4-1.

I Hate Childhood Friends: Same as above, unsure if needed to do in one playthrough.

Ladders vs Step Ladders: Unfortunately I didn't make a save for every single step-ladder conversation. I have two separate save files in two separate slots in the folder, and one more can be obtained from Set 02.

%-----------------
Set 01
1  The Lost Turnabout
2  Reunion, and Turnabout
3  Turnabout Big Top
4  Farewell, My Turnabout
9  Judge Wackner
10 Justice III Served
%-----------------
Set 02
1  Turnabout Memories
2  The Stolen Turnabout
7  Smells like Oldbag - Security Office -  List, purple bag, seat
8  Smells like Oldbag - DeMasque's Hideout -  transceiver and helmet
9  Stepladder, TT EP.2
10 Beware, Your Honor!
%-----------------
Set 03
1  Jean's Foreign Language Course - Part 4-1: Trial - In the Restaurant
2  Recipe for Turnabout
3  Turnabout Beginnings
4  Bridge to the Turnabout
5  I Hate Childhood Friends - Heavenly Gate
6  I Hate Childhood Friends - Present the Attorney's Badge
7  Violetta's Home-Made Donuts
8  Jean's Foreign Language Course - Part 4-1: Trial
9  Jean's Foreign Language Course - Part 3: Investigation
10 Jean's Foreign Language Course - Part 1: Investigation
%-----------------
Set 04
3 Turnabout Samurai
5 Turnabout Goodbyes
%-----------------
Rise from the Ashes
10 Rise from the Ashes
%-----------------
Secret Weapons Three
3 Secret Weapons Three
%-----------------
Naruhodo A Wrighto
3 Naruhodo A Wrighto
%-----------------
Um, Lotta Hair, Was It
2 Um, Lotta Hair, Was It
%-----------------
The Lost Turnabout
2 The Lost Turnabout
%-----------------
Mind Your Own Business
1 Mind Your Own Business
%-----------------
Please Turn In Your Badge
1 Please Turn In Your Badge
%-----------------
Lunchbox Specialist
6 Lunchbox Specialist
7 Lunchbox Specialist
8 Lunchbox Specialist
9 Lunchbox Specialist
%-----------------
Ladders vs Step Ladders
3_JFA_E3_slot3
5_TT_E5_slot4