Probably the hardest trophy in the game, which wouldn't be too surprising for any other game but for the most part the difficulty for the Platinums in Yakuza games are more for the side content as opposed to the main game. Not so here, I would say.
Dead Souls mode is unlocked by beating the game once on any difficulty and you are not able to carry things over via Premium Adventure; it's a fresh playthrough. Enemies are MUCH more aggressive in this mode and deal a fair amount of damage, and the most dangerous enemies in this difficulty are ironically enough your bog standard zombies. The game spawns hordes of them in this difficulty and they absolutely love to charge you which is an instant knockdown, to which they will then stomp and potentially stunlock you every now and then. As such it is vital that you get the skill which allows you to do a sweep kick upon knockdown, as this will help you escape from these mobs more easily and regain your bearings.
It's mostly useless trying to rely on the standard aiming of the game, so the shotgun is easily the best weapon for this difficulty (and in general, really aside from one boss and the Anti-Material Gun), as it has good crowd control capabilities and a fast reload and fire rate. Enemies will mob you on this setting so there is little point going for more ranged weapons. I would recommend upgrading it to the Flesh Shredder as soon as possible, which will hold you in good stead for most of the rest of the game. There's a situation late in the game where I would recommend the Assault Rifle, so aim to upgrade that as much as possible as well.
Now obviously you need money to do all of this, and in the EU version at least the game gives you plenty of tools to make a shit ton of cash very quickly that will more than tide you over for your entire run. Once you get to the safe area (probably on of the most difficult sections of the game in itself) and gain access to Kamiyama's Truck there is a guy sitting on the couch who will (in the EU version) give you a number of items including gambling cheat items, the most valuable of which being the Zero Jewel for Roulette and Player/Banker's Pieces for Baccarat. Get these and go to the casino (save beforehand) and with the Zero Jewel bet on either 0 or 00. You're guaranteed an 18 to 1 payout if you do the middle of these but it's a 50/50 chance to get a 36 to 1 payout so just reload the save if you don't get it. This alone will net you about 36,000 points (if you bet with 1000 which I recommend earning or buying from the clerk in the casino before this) and will allow you to buy more than enough Platinum Plates for the casino shop to sell to Ebisu Pawn to give you about 4 million yen which will easily last you the rest of the game. You will also get a fair amount of healing items from this guy and Bob B in Naomi's Palace. In the NA version I would recommend grinding points via Baccarat as that is the easiest and most lucrative method for that. Even just a few wins will give you more money than you need.
I wouldn't recommend going for Substories in this mode despite them being a good source of EXP considering the extra time and effort they take. Some of them don't take very long and Kiryu's are probably worth doing a few of considering the EXP yield but it is not really worth it and you will get more than enough EXP via playing the story even if you rank low in each story section. In terms of upgrades obviously go for Heat replenishment, weapon and armour modding skill, the aforementioned sweep move, item and particularly accessory space (There is a section very late in the game in which this is vital for). Getting the Ultimate Flak Vest via modding is extremely useful (Don't bother going for the Dragon Vest it is not worth the effort), as well as loading your accessory slots with defensive items as well (I think Tiger Belts are the best ones but I'm not sure).
Now despite your inventory carrying over for each character to the next you are not able to access it until you finish the first chapter for each character and get to the safe zone. As such, you are reliant on what loadout and items you get during that section and consequently the first chapters for each character are arguably some of the most difficult sections in the game (particularly Akiyama's and Goda's), so those are mainly the sections I will be covering. Once you get access to the safe zone and subsequently your Item Box you can get your previous loadouts and items and the rest of the character's chapter will be a lot easier by comparison.
Oddly enough one of the most difficult sections in the game is the very start. With Akiyama's opening segment from New Serena you are given absolutely no healing items until the first checkpoint and have to go through a series of buildings with swarms of zombies and a mandatory fight at the end. Death will put you back at the very start near New Serena. There isn't a lot I can say to help beyond dodge rolling and avoiding fights as often as you can and going for snap headshots in the mandatory fight. Once you get past that and get a healing item the rest of the section is a lot more manageable.
While I personally didn't die that much here Majima's first level can be tricky as well seeing as you can easily get swarmed while escaping the building. Thankfully his signature weapon is one of the best in the game and is great for crowd control. His boss fight with the Onraki prototype is also tricky and I would recommend using the tank when you can. Now one exploit that I haven't covered yet is the way to make Heat Snipes easier. In Dead Souls mode they are extremely difficult to pull off as you have such a small window of opportunity, so hitting the PS Home button will pause the game completely and allow you to see what button it is you have to press well in advance, as likely by the time you see it it will be too late to hit the button. Obviously you will have to mash it on and off a few times to slowly get you to the button prompt in that scene to pause and unpause the game. I say this now because this is when it really becomes useful and some boss fights are entirely reliant on you using Heat Snipes to end them (Majima and Goda's end bosses in particular).
Now here is what I would say is the most difficult section of the game: Goda's first chapter. It is long and tedious and you are entirely reliant on his Gatling Gun and items you earn during it. The most difficult section I would say is around the start when you go into that small building with the corridor and office room. In the corridor use the chainsaw charge attack (press and hold Triangle) to clear the debris and crowds of zombies (particularly the Aggro and Monkey Boy here). The next room is one of the most frustrating in the entire game, as it is a small room with a veritable army of zombies in it that will INSTANTLY rush you within a fraction of a second and knock you down. The fact that it is filled with furniture that will knock you down if hit at you by a zombie also does little to help matters. The Gatling Gun is ill suited for such an assault and as such this room is incredibly annoying. This is where the sweep ability I mentioned earlier is vital and I thoroughly suggest getting it as soon as you can via upgrades. When you do get knocked down and mobbed press R1 to do a leg sweep upon standing up and likely clear your immediate vicinity of zombies, allowing you some much needed breathing room and space to dodge out of the way and blast those zombies to death. Don't be surprised if this one room takes a few attempts. The next particularly tricky section is right at the end with the forklift. It cannot take that much punishment on this difficulty so you need to mitigate this. Once you solve the forklift puzzle (not going to go into how to solve that as you should likely know already; sorry if I'm being presumptuous) and on the way to the ammo crate are some zombies which you can run over but will damage your vehicle and leave you in a likely unfit state to withstand the hordes of zombies coming at you on the way back to the tank. As soon as you get past the puzzle and are given the prompt to get the ammo GET OUT of the vehicle and manually kill the zombies leading up to the ammo crate on foot. They will not respawn and you will save much needed health for the assault afterwards. Assuming you've done this you should get to the tank with just barely enough health left. If you lose all of your health in the forklift you will have to start the entire section again from before the puzzle, and we all know how slow and tedious that is. The rest of his chapter is much easier than this once you have access to all of your items.
Kiryu's opening chapter is much easier than this but can still be annoying (and hilarious) if you don't know the easy way to get through it. Kiryu is hilarious oblivious to the outbreak and tries to beat up the zombies with his bare fists, which results in the only three fist fights of the game (which are futile). You will need to "kill" a set number of zombies to trigger the end of each sequence and the easiest way to do this without being mobbed (too much) is to do the running jump kick (run and press Triangle) to instantly knock them down and register it as a "kill". His entire chapter isn't easy, really and the third and fourth part in particular are infuriating. If you haven't already get the Ultimate Flak Vest (second best armour in the game) and as many Tiger Belts as you can carry (which is why I suggested upgrading your accessory slots. Do a few substories at this point as they are very lucrative EXP-wise) and equip them. Create a separate save slot here in case you fuck up with something as you will not get time to restock for the fourth part. At the start of the third part where you and Akiyama have to hold out for three minutes there is very little point in doing anything other than dodging, sweeping and healing. You will very quickly get mobbed regardless and at every minute interval the current mob will clear for a new one, so endure this as best you can. The next fight with the Basan Prototype is probably the hardest in the game on this difficulty, largely due to it being a ranged fight. I thoroughly suggest (as I did earlier) to invest in the best Assault Rifle that you can and camp in the park (I find the Sniper Rifle useless but it's up to you). The zombies he spawns in the second part of the fight are literally endless but there is a limit to how many that can be in the game at once, and they will for whatever reason not venture into the park if they didn't spawn there. Use the Assault Rifle to hit his weak spot from the park when you can get a lock on him. He will likely go beyond your zone (a building blocks about half of the area) and heal a couple of times so whenever you see him attempt this shoot him to stop it. Persevere with this and you will get it eventually. Bring a lot of ammo for the assault rifle obviously.
Now the next section is what many consider the most difficult of the game on Dead Souls mode. You will be immediately forced into this after the previous boss fight so if you are ill-prepared reload a separate save before the third part and get better prepared, as you will need it. If you haven't already done so get the Ultimate Flak Vest and as many Tiger Belts as you can carry, as despite it not making a lick of sense all of your equipped item's capabilities will be applied to the tank you re in. You are in a tank on the way to the weaponsmith for an on-rails segment with no way to heal and with a particularly persistent Onraki prototype chasing you for most of it. For the first encounter there is honestly very little you can do. Even if you wipe out its health bar it is a timed section and it will not end until that time runs out, which is incredibly fucking stupid and beggars belief why he even has a health bar to begin with if it doesn't matter in the slightest. If you can get a few stuns off that is immensely helpful for the latter sections but don't worry too much if you don't. Once this is over and after a bit more driving the Onraki will chase you and attempt to rush you, which will deal shit tons of damage if it hits. If you can even prevent one of these from hitting you it is an enormous bonus and will likely save you, otherwise I'd say you will likely not survive the end of the section and have to start again.
That's about it for the difficult sections of the game. The final chapter isn't that hard with the Anti-Material rifle and enough healing items. A final tip would be to just avoid combat as much as humanly possible, dodge as much as you can and only fight the fights you are forced to. Good luck and I hope this helps someone!