A Fresh Start: Chapter 1: Give the homeless man the 20k booze from the bar instead of the beer from the peddler
Good With Kids: Chapter 2: When prompted to help with chores at the orphanage, sticky hand from the peddler to help with tidying, fancy detergent from Mina's apartment to help with laundry, go to the botanical garden to help with homework
Mina's First Time: Chapter 3: During the showdown with Mina, beat her after whipping yourself without using the poison (it's not that hard, she'll fold if there's any chance of losing)
My Desert, My Dune: Chapter 4: You'll be prompted to take an offering or take cash from opponents on the event stage, always take the offering (Did it at least 3 times) Also when the robot is exploding choose to push it away (unsure bout necessity but I'll include it anyway)
Database Access Log: Chapter 5: After the final boss fight when prompted by Mini choose for them to GO AWAY
Until We Meet Again: All of the above in one run

[NO LONGER RELEVANT] Poker Royale was updated to have less runs required

Here's what I did:

Always have Sharp Eye+ for intel and Luck of the Draw+ for better starting hands.

5 run: Abused Luck of the Draw+ and all-ined any time I got a pair.
10 run: Same but with more attempts.
25 run: First of all it's actually only 20 long so at least there's that. Here you can start abusing Sweat Em' (force opponent fold, + isn't necessary but helps with upkeep) and Bide Time+ (2 Luck now to generate 5 later, will not generate if used during hand that beats opponent, + IS VERY necessary for upkeep). When you have more than double the chips of your opponent if you all in and force them to fold, they automatically lose whether or not they've bet any chips so all you're trying to do is make sure you have enough luck to force the opponent to fold if you're ever going to lose a hand.
50 run: Same as 25 run cept there are some checkpoint opponents with marginally more chips.There's also a boss for this run with i think like 30 mil chips? I purged my memory of this almost immediately but I bet the same thing works here from the 99 run
99 run: Same as 50 run except the last challenger has 50 mil chips, same as what you have starting out so you need at least the same amount of chips, luck capacity to Sweat Em' twice in a row and need to bet some chips in the initial force fold since force folding causes the opponent to lose a little less than half their chips. Then force fold again and you've won.

If you're ever running low on chips, you can spend some rounds adding Deep Breath+ to regain some chips when the mult is low.

These are obnoxiously long and filled with mostly the same 5 mil fodder opponents that you can force fold into oblivion. THERE ARE NO CHECKPOINTS so if you lose at any point you have to start over from the beginning.

If the devs ever change Sweat Em' to not take out these opponents, god help anyone who attempts this.

If the Until We Meet again achievement requires this, I'm so so sorry.