Your loadout should be Aged Feather Mist Raven/Loaded Umbrella Magnet, Purple Fume Spark, and Piercing Sabimaru. You should also have Healing Gourd, Fistful of Ash, Ceremonial Dagger, Pellet, and Gokan's Sugar in your quick items. If you prefer not to use Ceremonial Dagger, I would recommend also dropping the Pellet and swapping them for Eel Liver and Bite Down. For CA you have your pick of Floating Passage, Whirlwind Slash, Ichimonji (double if you want, doesn't matter), High Monk, or Mortal Draw/Empowered Mortal Draw.
Healing Gourd: Obvious. Drink this to heal. Very dangerous to do this against Isshin however. That's why we have Purple Fume Spark. Isshin will cover huge distances to punish you for healing, and his AI seems to react to you activating the Gourd. Ordinary Fireworks have a habit of going off a little too quickly to catch him when he does his dash-in attack, so Purple Fume is a bit better. Either can work though, just with stricter timing.
Fistful of Ash: Doesn't work on Isshin, but it does work on Genichiro. Specifically, it prevents him from charging up his Mortal Strike and from continuing his very long, multi-hit combo. By now you should be able to recognize the startup for both of those attacks. Keep Fistful of Ash as your active item during this fight so you can throw it as quickly as possible. Obviously this is another opportunity to heal against Genichiro, and it's better than Fireworks since it saves you emblems for Isshin and also because Purple Fume Spark is actually a bit slow against Genichiro.
Ceremonial Dagger and Pellet: Four phases is a longer fight than anything else in the game. Ceremonial Dagger will prevent you from burning through too many emblems and getting stuck. Pellet just heals the dagger damage without wasting a Gourd charge.
Gokan's Sugar: Safer blocking against Isshin's long combos. Activate this in between phases. If you need to re-activate it mid-fight, Purple Fume Spark is the way to do that.
Bite Down: Don't die the ordinary way on Phase 3, if you can help it. Bite Down allows you to resurrect without requiring another Deathblow to reset your charge. If you plan to use this strategy you should always just L1 your deaths on Phase 1 and 2. The best way to use this is immediately after poisoning Isshin with Sabimaru. Wait for five heartbeats then resurrect so he takes as much poison damage as possible, then poison him again.
Eel Liver: Phase 4 is all about Lightning Reversals. Use this immediately after the deathblow in Phase 3.
Aged Feather Mist Raven/Loaded umbrella Magnet: I prefer Mist Raven but either works here. Both bosses have projectile attacks that do huge posture damage when guarded, it's better to just use a defensive prosthetic tool. Genichiro damn near kills himself with his long combo if you deflect all the hits with Umbrella, but that shouldn't be necessary if you're using Fistful of Ash. Mist Raven is a little better for Isshin specifically, since it can be hard to predict his gun attack and you can activate Mist Raven as soon as you start blocking or taking damage to save yourself. It also gives you a better out when he does his sheathed Ashina Cross attack, as you can teleport to the left or right for an easier time dodging the follow up. Wait for the glint, then activate.
Purple Fume Spark: Purely to give yourself a breather and find the time to use items mid-fight. Don't go crazy, here. You really want to conserve emblems for Sabimaru, which is the single most effective weapon against Isshin.
Sabimaru: Isshin is vulnerable to poison. How cool is that? You never see a final boss that has status vulnerabilities. This is the best way to chip down his health so that you can actually start to build his posture meter, short of just memorizing his moveset and perfectly deflecting everything. Bite Down helps here, as I said, to buy more time for the poison to do its work. You should have plenty stocked up since there's only like three other places in the whole game where Bite Down is useful. Otherwise, the Hidden Tooth does the exact same thing if you found it. Isshin only has one or two attacks that can poise through Sabimaru hits; most of the time he will stagger until the full combo is complete. You should use the follow-up attack as soon as you see the poison status activate or not at all, as he'll punish it in every other case.
Combat Art: not many opportunities to use this in the fight. After a lightning reversal you can get anything you want, including the bigger charge-up attacks like Mortal Draw and Ichimonji. I don't really like spending emblems here but its an option. High Monk lets you high-profile all of his horizontal wind attacks in every phase (you can also use the conventional jump kick attack to get above them, if you're close enough) and punish his gun attacks if you can predict them. Do not use it after his Ashina Cross, as the attack is 100% vertical and will catch you anywhere in the air. Floating Passage is a bit of a cheese strat for Genichiro and Isshin's first phase, both of which are vulnerable to staggered attacks with slight delays between each hit. Whirlwind Slash lets you chip through Isshin's insane blocking but make sure you do it at the end of his combos in Phase 2 or he'll easily punish it.
The basic rule with all forms of Isshin is that you don't want to actually let him get a deflection on you. In most cases this means attacking one time only. There are very few bosses in the game that punish you for wailing on them until they're forced to deflect. Isshin is the exception. It's generally safe to go for two hits if you're using Whirlwind or Floating Passage, although both have issues. Your basic gameplan is to attack once and then deflect the next thing. Once you get this pattern down the fight is just as trivial as anything else you've learned how to do. Each phase has its own rhythm and surprises but it's hard to spell out exactly what to do next until you can feel it in practice. One hint I'll give you for Isshin's first phase though is that you can stuff the PA he does after the first attack if you wait a beat. He'll start walking to your right, you'll see the PA icon, and just hit R1 again to stop the attack cold and get some free damage.