The first boss you encounter in Nioh 2 is Mezuki, a large horse-like demon with a massive sword ready to slice you up. While he's tall, he's a bit clumsy, giving you a handful of chances to get in close and deal big damage to him. But, if Mezuki hits you, you are in a world of pain.
Mezuki's most notable attack is those two dark explosions he shoots from his mouth that look like dark spirits rushing at you. You want to dodge them because they damage you, but when they land they create ground ki disturbance, making it harder to recover your ki during combat. You want to avoid these areas after ending an attack, or you won't be able to escape. Mezuki also has three massive strikes in front of you, you need to dodge. After these attacks, he is vulnerable for a while, which gives you a chance to attack him.
He has an attack that you can use the Burst Counter, where he hits down several times, moving forward. You can use that time to rush and do the counter, but if you miss the timing those massive strikes will fall on you. Alternatively, another attack you want to watch out for is its charge, on which you can also use the burst counter to deal damage.
You don't want to stay too close to Mezuki as he has a pliers that grabs you in the air and cuts you with his sword. You can anticipate this grip indicated by the black and white aura of her left hand when she reaches for you. Also, you can't stay behind Mezuki for too long as he has a back kick that knocks you away. The best strategy is to jump, do a handful of punches, wait for him to attack, then roll to avoid damage and get your ki back.
After lowering Mezuki's Anima once, the right arm bursts and becomes stronger. His attacks change and become more aggressive towards you. Now there are three Dark Blasts instead of two coming out at you, and he swings his sword further against you. You want to dodge these attacks and get closer, waiting for Mezuki to charge you up and counter him. You can pepper in several mid position attacks, using your outside strikes to beat him. This mode won't last forever, and when it ends, Mezuki returns to normal, but when you lower his Anima, he returns to that form.
If you can reduce the distance between you and Mezuki quickly enough, such as using pliers to get closer after he hits, you shouldn't have a problem taking him down. You don't want to use all of your ki in a series of attacks because it exposes you to them.