Hey, I don't know if anyone has ever posted a playthrough before but here's mine with a guide to playing the game as PERFECTLY as possible:
Day 1: On the first day you can't defeat anyone. You'll start in a mine arena though and there'll be a huge hole at the bottom you can enter to a tunnel. In it there's a pickaxe which you'll have to pick up and equip. This is as far as I know the best weapon you can get in the game and even better than the most expensive melee weapon you can buy at the blacksmith (it has slightly more defence and agility but slightly less attack, like 2-3 points for each stat). Fun fact: with this you'll be able to defeat Lux in the FIRST BATTLE though the game puts your HP to 0 regardless after her attack. You'll see the game bug and see you'll be left with 30 hp after Lux's final attack though the game will set it to 0. As to the decision you get what to say after Lux upon beating her, idk if this matters. I haven't noticed a difference no matter what u say. Once this is done, just go towards the inn to ask if you can get a room after this you'll get the tent. You don't have to talk to anyone else or waste any further time on day one and can go to bed immediately. Also go to the inn upstairs to get the health potion. I've never found an use for it but I can't afford knowing I skipped over it when I ever do need it mid-battle.
Important notes: Deal as much damage in fights as possible, you need to go for the very well message at the end of the battle which gives u 150 gold. Also as obvious as it is collect every chest in every arena. One has 2 so look around before defeating everyone.
Day 2: This day starts with some kind of thing at the inn. Idk if you have to do this or can just immediately start the fight. I just always go to the inn to see what's up. After this thing go to the blacksmith -> ask about -> ask for a discount and then go out to start the fight. You have to do this so you can return the next day to unlock the getting the ores quest. Now start a battle, On this day tell Lux the truth during the arena fights. Your opponents also start off weak in the begin and slowly get stronger through the game and you'll find with the mining pickaxe you can get people like Katarina already to 412/1250 hp. As for Lux's binding light attack, I believe you have to literally not struggle as she said. This is an attack that fades after 2 turns and can't be struggled through so just guard yourself to minimize damage. Also idk if it matters but I do this on every speedrun, after the battle talk to Katarina once just to get the bullshit text she says away in preparation of asking her if you can train on the dummy some days later. If this has impact, idk, but just do it in case you need to reset your safe. If you fuck up too much shit and your opponents get too strong it'll be impossible to defeat someone and you'll be stuck playing the game just receiving story content thinking you're doing something good.
Day 3: Wake up and go to the armory to unlock the ore quest as I said on day 2. It'll active the ores quest and let you collect ore. Start the battle, if Irelia tells u to bow down to her or not I don't know what the decision is and if it impacts anything. My multiple playthroughs don't show a difference. I'd just not bow down to anyone since that can sometimes affect how u perform in battle. Lux's decision doesn't show a difference either as far as I know. I have a feeling she goes harder on you though if you say you can beat her though I have absolutely no clue if that's the truth. I'd have to go through too many playthroughts to know. As for Katarina, refuse to kiss her ass to keep fighting and deal as much damage as possible for the very well 150g message. At the end you can make a run for it to get an unique picture. Once the battle is done talk to Katarina and refuse begging, then go to Lux to have your first training. Idk if magic does anything good in this game, I believe you can train it through multiple use though idk if it's worth the time. After this all you should be able to have enough money (700g) to buy the 700g chain vest. After this go to the inn to watch another scene and defend yourself (no idea if it has any difference). The game then hints I can use their rivalry against each other though I have no idea how to do that lol. After this go to bed and don't jack off to Katarina. You want to keep your fixations as low as possible because it'll make it harder to resist your opponent in battle (Katarina's ass sway attack for example will succeed no matter what if you keep pleasuring her to train later on).
Day 4: Start the fight and refuse to kneel to Irelia and refuse to be her peasant. To Katarina say you're going to beat her and continue the fight then refuse to kiss her ass again. After the battle sleep till evening, go up to her and offer to clean her up to train on the dummy. After this go to bed.
Day 5: Go to the inn and say you'll beat her then go into the portal to start the next fight to unlock Qiyana. At the start when she tells you to bow down, say no and start the fight then start bowing down to her if she commands you during the match. Not doing this will increase her attack unless she asks you to die. You can't win this fight despite being stronger because she has some dumb move which grants her 700hp if she's about to die. After this day don't ever fight her again and just avoid her on the battlefield because it's a guaranteed loss and she can eventually start taking your money too. After the fight check what the fight between Irelia and Katarina is about and then start your next lesson with Lux. The answers are Taryen, peacefully, ishnu yelegan, and the mage itself. Doing this all succesfully grants you another magic attack you're not going to use another day when you approach her again. After this all it's the evening and you can make good on cleaning Katarina by finally training the dummy and getting to level 2. If you're able to do another fight on this day with the 3 opponents I have no clue but it's now night.
After this it should be smooth sailing through the rest of the game.