This boss fight is pretty straightforward and that Martyr Logarius doesn't employ cheap tricks. His movesets are limited but he can be aggressive as the fight goes on and can build enough pressure to break your composure. The fight can be very manageable and people having doing it even on BL4 runs.
Quick Notes
Weakness is lightning so Bolt Papers are a must but optional. You can also use Tonitrus is you have an arcane build. Evelyn works perfect if leveled up but a Blunderbuss can do the job as well especially if you have your parrying timing off.
Phase 1
Best way to start the fight is get up and close to him. If he swings his scythe around then just dash forward to him ignoring the floating red skulls. Land at least 2 hits then back away before he summons a larger red skull that does aoe damage. He will sometimes attack you with melee attacks and there are opportunities for staggering here. If he does the slam his scythe on the ground then there's also a window to do a charge attack from behind before a visceral attack.
Just Before Phase 2
Martyr Logarius will slam his scythe on the ground and will start to charge up. This should happen if you have at least chipped away 35-40% of his HP bar. When it does happen, quickly go around and perform a charge attack on his back to stagger him and apply a visceral attack. If you let him charge all the way through then he will be immune to bullets for the rest of the fight and it'll be harder to parry him.
Phase 2 and 3
The fight then becomes much more physical and Martyr Logarius will start flying upward before lunging forward with his scythe. Best way to avoid is the quickstep forward or sideways. You can roll but quickstep is much better in this scenario as it keeps you locked on him. You can gun parry his lunge attack but it's risky if you're not confident with your timing. Best is to watch out for his close range attacks, this is where you'll get plenty of chances for a gun parry. Lastly, if he is around 30-40% HP remaining, he will start placing a red spectral sword in the ground which will become annoying as several flying swords will start to attack you (homing too). As soon as he does this, quickly shift your auto-lock towards the sword and shoot it with a pistol. Rinse and repeat the rest of the steps here and take him down easy.
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#MartyrLogarius #Bloodborne