No self-respecting third-person action game misses an enemy that follows the Wukong archetype. In Nioh 2, that enemy is Enki, and this is your first introduction to the interesting position the game has with certain enemies. Complex moves, special abilities, and burst attacks aren't limited to just the bosses in this game. Enki feels like a boss and fights like a boss, but he's just a regular enemy.
Enki is a bit more embarrassed in this first fight because there is limited space to engage him, so be careful around your surroundings and don't get caught up in the terrain.
The trick to dealing with Enki is to dodge quickly and keep a perfect range. Enki hits pretty hard at the start of the game, when you first meet him, so dodging attacks is a better option than blocking them. For the most part, his attacks are well telegraphed, as he pulls his long spear to slide or slam you, giving ample time to dodge to the right, as his attacks swing from top right to bottom left or from bottom left to top right. Try to keep yourself in that security pocket, to ruin yourself when you can.
Don't get too close, or his attacks get a little harder to read, and don't stray too far because you want to stay in a good range to Burst Against his attacks. When you see it glowing red, that's when you detonate Counter. Wait too long and Enki will have already taken off and will more than likely slap on you. Keep a medium range, and Burst Counter instantly to deal massive damage, and get a large window to deal even more. Hit a few times, then dodge back and circle, and be sure to sync your Ki well to regain your stamina.
One attack that you should be very aware of when fighting Enki is that he will jump into the air and then throw his spear at you. When you see it leave the ground, instantly block. The spear throw attack has pretty aggressive following, so single block is the best option.
Once you defeat Enki, you will get the Enki Soul Core, granting you access to the Monkey Dance Yokai ability.