Martyr Logarius is the boss of the hidden Cainhurst area of the game (see the "Cainhurst" trophy to see how to get there). This is one of the toughest areas in the game, so do not attempt this until you are quite high level.
This boss has a long scythe and also frequently casts very dangerous spells. He moves quickly, so you will have to be cautious with your attacks. Use the quick one-handed version of your weapon, and do not try to get more than 2 or 3 hits in at once. Try to stay behind him at all times, as this will avoid his deadly frontal explosion spell.
Once he gets down to about half health, he will sometimes place a sword in the ground. As long as that sword exists, swords will home in on your from the sky, making your life miserable. Simply attack the sword in the ground once to destroy it and stop this from happening. Then continue with Logarius as you had been before. See the following video guide: