A couple more weeks into Sekiro, and I'm still nowhere near being finished with the game. I'm definitely getting the hang of it more, but am also still struggling at pretty much every boss (and mini-boss) that I come across.
I have a few tips based on my own experience and observation that I hope will be helpful for other players, so that you don't have to go through some of the headaches that I've gone through when adjusting to this new game. As stated, everything I'm about to say are my own personal tips and observations. Do not take any of them as gospel. In fact, if you have your own tips, I'd love to read them in the comments.
There will be some minor spoilers for early game content.
Bank your sen
First and foremost, you should definitely take advantage of the ability to "bank" your sen (money). This is one area in which Sekiro actually offers a bit of leniency to players who may be familiar with Dark Souls. The Souls games did not allow you to directly bank your souls; but Sekiro does have a way to bank your cash.
You can use a Light Coin Purse to acquire 100 sen, but they cost 110 sen to buy.
Most vendors will sell coin purses (in varying sizes). Now, you may have noticed that the vendors sell their coin purses for 10% more than what they are worth. For example, if you use a Light Coin Purse, you'll receive 100 sen. However, it costs 110 sen to buy a Light Coin Purse. Similarly, the Heavy Coin Purse grants 500 sen when used, but they cost 550 sen to buy. There's a 10% mark-up.
Sadly, there's no bulk discount for buying larger coin purses, so there's no reason to save up for the Heavy or Bulging Coin Purse, as opposed to just buying a bunch of Light Coin Purses. The number of coin purses that each vendor will sell is also limited, so invest wisely!
Dying will take away 50% of your un-banked sen.
Don't let this 10% mark-up deter you from buying the coin purses. These coin purses are not lost when you die, but some fraction of your "soft" sen are lost when you die (unless you receive "Unseen Aid"). If you do not intend on making purchases with your coin in the immediate future, then you should strongly consider banking the sen by buying coin purses -- especially if you are about to enter a new, unfamiliar area, or if you are repeatedly dying to a boss or mini-boss. A single death will cost you 50% of your un-banked coins. Repeat deaths will quickly eat away at the rest. And (unlike in Souls-Borne), you can't go back and retrieve your lost coin or experience. The 10% mark-up on buying coin purses is a paltry penalty in comparison, and the insurance of having coin purses is well worth the investment!
There are some very expensive items in the game, and upgrades to the Shinobi Prosthetic will cost hundreds of sen (or more) each (as well as the cost of the upgrade materials, such as iron or gunpowder). You definitely want to save up your money!
If a vendor won't sell any more coins to you, then you should instead consider spending as much of your money as possible on other items such as Pellets, balloons, sugars, or whatever else the vendor may be selling. If all else fails, then you should bank your sen on Spirit Emblems at a shrine if you are likely to die in the ensuing level. Your money doesn't do you any good if you lose it all from repeat deaths!
There are some expensive items and upgrades that will require you to save up sen.
You don't have any way (that I'm aware of) to bank your skill experience other than to buy a skill. However, banking skill experience isn't as necessary as banking money. You only lose skill experience accrued beyond the latest skill point(s) already acquired. So if you are (for example) 99% of the way to your fourth skill point, and you die, you won't go down to having less than 2 kill points; instead, you'll only be down to 50% of the way towards that fourth point. You'll still keep (and be able to spend) those first three skill points that you already accrued.
If you get stuck, experiment and explore!
Sekiro is a highly explorative game, and it has secrets hidden all over its nooks and crannies. I've explored off the beaten path and found entire levels that I had no idea existed! Even when I wasn't finding whole levels, exploration would still often reveal new Shinobi tools, merchants, and upgrade materials that may help give me an edge in combat.
If you're stuck at a particular boss (and I've gotten stuck at pretty much every boss!) then I recommend that you take a break from banging your head against that boss, and go explore the map some more or search through your inventory for something that may be useful. Almost every boss in the game (that I've encountered so far) has had some weakness or vulnerability to some weapon, item, or skill that Wolf possesses. If you find yourself drinking from your Healing Gourd repeatedly, while only shaving off slivers of the boss' health or posture, then you're probably missing some trick or tactic for beating said boss.
First, you should check your own inventory and skill list to see what you already have available to you. Experiment with different Shinobi Prosthetic tools (after banking any sen!). Maybe you'll find that the boss is weak to fire, is easily stunned by the fire cracker, can be knocked out of a jump by a shuriken, can have armor peeled off by the spear, or so on. You should also check your inventory. If a boss is vulnerable to fire, then combine the Flame Vent prosthetic with Oil Pots to deal greater damage. Other items in your inventory may provide you with other advantages against other bosses. Just be careful about spending those items carelessly, or else you'll have to go farming for more.
If a boss comes with a tutorial tip,
you should probably pay attention!
I've had instances in which I tried and failed to defeat a boss over 20 times before finally trying some different Shinobi Tool, finding that it works brilliantly, and then went on to beat the boss in just one or two more attempts.
Secondly, check what skills you have unlocked and experiment with different skills. Some bosses will even have tutorial tips that pop up explaining how to use certain techniques. If you see such a tip, then you should consider it a guarantee that the boss will be susceptible to that technique, and that using said technique is the recommended way (by the developers) to beat the boss.
To this point, I highly recommend that you invest in the Mikiri Counter (from the Shinobi Arts skill tree) early. This skill allows you to counter thrusting attacks from enemies and bosses (attacks in which the red glyph appears as the enemy attacks). Successfully using this skill will pin the enemy's weapon under your foot and allow you to make a devastating counter against their health and posture. Other bosses or mini-bosses may be easily defeated with other techniques, such as side-stepping and countering, jumping over them, or so on.
The Mikiri Counter Shinobi Art is one of the most useful skills in the game!
If all else fails, then it might be time to take another run through the levels. Check off the beaten paths for secret areas or other levels that you may have missed. These areas or levels may contain some useful item or a Shinobi Prosthetic tool that can make mince meat of a boss. For example, the Blazing Bull (which I had written about previously) is easily stunned by the Shinobi Firecracker, which is created using Robert's Firecrackers, which can be bought from the Memorial Mob vendor on a cliff in the Ashina Outskirts. Similarly, the Chained Ogre is vulnerable to the Flame Vent prosthetic, which is derived from the Flame Barrel item found within a bonfire in the early sections of the Hirata Estate.
Items hidden in levels, or sold from vendors, may provide weapons for certain bosses.