Esgar is very similar to the Bloody Finger Nerijus NPC invading you in Limgrave, and even uses the same Reduvia weapon and its skill Reduvia Blood Blade. Of course, there is a twist: two very angry dogs will be assisting Esgar.
Both Esgar’s and his dogs’ attacks will cause some Hemorrhage build up, so equipping Armor/Talismans with higher Robustness will help you mitigate damage.
The dogs have very little health, so focusing them first is a reliable way to facilitate this encounter
This fight is very similar to a regular NPC invasion, and Esgar, Priest of Blood behaves almost exactly the same way. The difference here will be that Esgar will be helped by a couple of dogs that also cause Hemorrhage, and he will not be able to heal himself during the encounter. You on the other hand will be able to use your summons, which is highly recommended for this fight.
You have two ways of approaching this fight: kill the dogs first and then focus on Esgar, or focus Esgar, whose death will cause the dogs to die as well. The safest option is to kill the dogs first, as they will be by far the most dangerous part of this fight. And while you’re used to dealing with dogs by this point in your playthrough, these dogs can have an attack chain of up to 4 attacks, all of which inflict Hemorrhage. With that in mind, you want to either attack at the end of their attacks/attack chains, or catch them off guard while they’re running towards you.
As for Esgar, the most effective way of dealing with any NPC invasion, is simply to create some distance between the two of you, and use one jumping heavy attack at a time every time the NPC starts running towards you. Of course, you can also just stagger the boss by attacking him repeatedly, though he will still be able to punish you at times.
If you’re ranged however, while it may prove difficult to hit the boss with his dodging, using a spell inflicting damage in a wide area, such as Dragon Fire, will make it much harder to avoid.
Lastly, if you’re having trouble dodging the boss’s ranged attacks, don’t hesitate to use the pillar found in the boss room as cover. And while the Blood Swarm spell the boss will use can be hard to dodge, dodging through it will be the most effective way of avoiding its damage.