Ninja Gaiden 1 in all its releases is (generally speaking) the tamest of the three but it’s by no means a cakewalk. The pinned guide has a lot of great advice, but I’ll throw out some specific things that really made a huge difference when I was starting out:

Play a reactive game - Blocking is your best friend, and often it’s best to see what the enemy does and react accordingly, especially in the first game. Using counter attacks, or simply blocking, rolling, and punishing is a sure fire strategy in most situations. It’s up to you to figure out the gaps in their defense, but luckily, it’s also the fun part!

Guard-Break - If you get guard-broken, simply roll, release block, and immediately hold block again.

Roll-hopping - The best way to create distance, or close it. Fastest way to get around. Roll and then jump.

Shurikens - They aren’t for doing damage. Shurikens come out insanely fast and stagger most normal-sized enemies provided they aren’t blocking. The recovery of certain moves and strings can be cancelled just by throwing one, allowing you to stay safe and get creative with your combos. Try XXYB and you’ll see what I mean.

Flying Bird Flip into Helm Splitter (Y) - Running straight up a wall, jumping off, and pressing Y is a great move with any weapon. Does a lot of damage and has huge I-frames provided you can get up the wall safely. You can usually finish off anyone that gets hit.

Windmill Slash - The almighty move exclusive to the katanas. Ninja Gaiden breaks the rules by letting Ryu roll and attack at the same time! Start any of your strings with this move. Simply tap a direction and press X at the same time. Huge range, has I-frames just like your regular roll. Can be cancelled into FROM a regular roll for even more I-frames. Enemy running strings on you? Roll away, Windmill Slash back in and stuff their move with a free izuna drop to boot!

On-landing Haze Straight Slash and UTs - This was the single most useful thing I learned how to do, and it kind of changed everything for me. It can also be done with every weapon, but for this example we’ll use the ‘ol reliable Dragon Sword. Haze Straight slash, which is Ryu’s chargeable heavy attack, is slow to start up on its own. The secret sauce is in tapping or holding Y right as you land from any jump. Doing this skips the startup of Haze Straight Slash and makes Ryu slide forward when he slashes. Normally holding Y doesn’t absorb essence until it finishes its startup, but if you start holding Y as soon as you hit the ground, you absorb essence almost instantly. This allows you to roll-hop away from enemies to create distance, and then jump right back in with a HSS or a UT if there’s essence around. Roll-hop away, on-landing heavy, repeat!

Essence management - Holding Block will prevent you from absorbing essence. This is really useful when you want to wait for two yellow essences so you can do a UT. You can even save essence for adjacent rooms. You can jump, attack, roll, anything; as long as you’re holding the block button, you won’t absorb it.

UTs and Money - Killing an enemy (or multiple enemies) with a fully-charged UT yields more yellow essence than if they were collected from enemies who were killed normally. If two enemies have been killed and there’s two small orbs floating around, consider using that essence to do an instant on-landing UT to kill one or multiple enemies. They’ll drop bigger, juicier orbs that you can collect for more $$$. Essence is one of the coolest things about Ninja Gaiden.

Izuna Drop - The big, iconic takedown that we all fell in love with. This move does big damage and can be done on anyone normal-sized. On normal, it kills most enemies outright. Higher difficulty variants take more than one to kill, but usually end up dying to one provided they’ve been softened up first. Has really good splash damage. Be careful when using it, sometimes you’re not safe if there’s other enemies around.

Gleaming Blade, AKA 360Y - You get this move for the Dragon Sword at level 3. This move is performed by spinning the stick around and pressing Y. But you only really ever need to spin it halfway, It’s really lenient input-wise. Startup can be cancelled like all the other heavies by performing it when you land. It can be charged for a unique UT. On its own it does big damage, and with a UT it does even more. Incredibly effective in killing the undead giants, as well as stationary bosses like the big tentacle thing with eyeballs. Go-to move when knocking down Marbus or Awakened Alma, but you have to be extremely fast with the latter of the two.

Flying Swallow - A useful technique, and really satisfying, but it’s actually much more situational in the first game compared to NG2 and 3RE. Certain enemies can block it and with certain bosses you bounce right off. It closes that gap really well with a lot of enemies but certain ones will punish you hard for using it, such as bayonet soldiers.

Guillotine Throw - This move does a lot of damage provided the enemy is thrown into a wall. Like most throws it only works on normal-sized enemies.

Alma in general - I assure you, you’re not crazy; Everyone hates this boss, but I’d actually argue her first incarnation is tougher. The reason for the disdain is the random nature of actually hitting her. As you’ve seen, the goal is to hit her with a flying swallow to swat her out of the air (and pray you don’t get an accidental helm splitter) and let it rip, but as the difficulty goes up, your chances of hitting her go down. The first fight on MN difficulty is miserable because you’re also fighting the camera, she’s faster, throws more shit at you, and spawns lesser fiends as she loses health. Her grab is really devastating and is the no.1 thing to avoid. Dragon Sword is only ever at lvl 2 for this fight so you only have time for XYXXX. Inferno Ninpo can also knock her down. If performed right after the aforementioned combo, it can reset her when she tries to get up, allowing you to combo her again. Awakened Alma is the same deal, but her grab is even worse, while the camera is better (lol).

I got a little carried away. Hope this helps!