Aldrich, Devourer of Gods is your next Lord of Cinder, and we're going to use his full title whenever we refer to him because he earned it, dammit – in fact there is speculation that you fight him whilst he's mid–devour, and that the womanly torso sticking out of the top is actually a god being consumed.
Aldrich, Devourer of Gods was apparently eating people way before he became a Lord of Cinder (which happened against his will, because someone said 'Hey, let's lock up that really powerful slime monster that eats people alive and force him to sacrifice himself to the flame, thus making him even more powerful and insane than he was!' and nobody objected to that), so you can terminate him with extreme prejudice. That's easier said than done, though. Aldrich, Devourer of Gods can be a very frustrating fight.
Aldrich, Devourer of Gods is at the back of the Anor Londo cathedral, and there are two ways you can run through. If you've opened up the cathedral front doors then you can run up the stairs and straight through, with the disadvantage there being that the deacons at the end will see you sooner and have a longer time throwing fireballs at you.
The other option is to ignore the front doors and run around to the left side entrance, up the stairwell and into the side of the cathedral, then run up and around the walkway of the cathedral to the other side. This means that the deacons won't be able to see you for as long and you can avoid some fireballs. The disadvantage here is that it takes longer. Either way you need to run up the stairs at the front of the cathedral and either avoid or fight the silver knights there. If you run and dodge on the left side of the stairs, then the first knight's attack with his pike won't hit you.
Before you start your run think about items that increase your magic and dark resistance, but mostly once that increase your stamina, because you're going to have to do a lot of running around in this fight.
Aldrich, Devourer of Gods does most of his damage at range, so get up close if you can. He uses ranged spells like homing crystals and soul spears when you're at range, which do more damage and are harder to avoid than the melee attacks with his big magic stick, which you can more easily dodge under, or avoid entirely by moving behind him. Aldrich, Devourer of Gods is also a fan of bodyslams, but there's a pause before this where he raises up to execute it, and his body is his weakest area, so at this point he's vulnerable to being staggered if you hit it. He'll drop to the ground and give you a long opening to attack here.
The melee attack to keep an eye out for is when Aldrich, Devourer of Gods summons a scythe, which sweeps in a wide arc in front of him. It drains a fair amount of your health and gives him back some, but is pretty easy to dodge.
After you deal enough damage in one go Aldrich, Devourer of Gods will disappear into the floor, prefaced by Aldrich, Devourer of Gods raising both arms staff straight up into the air. When he slams the staff into the floor he'll sink down, but the process will deal some some area of effect damage to you from around the base of Aldrich, Devourer of Gods, so back off when you see it happening. Head to the middle of the room and wait for him to appear again. When he does, close the gap as quickly as possible to stop him casting his ranged attacks – he often appears in roughly the opposite corner to where he was when he vanished.
The main thing to worry about is Aldrich, Devourer of Gods' cheap, cheap, cheating rain of arrows attack. If you see Aldrich, Devourer of Gods drawing a glowing arrow and aiming it up in the air then you know it's coming, 'it' being a rain of hundreds of arrows that will chase you around the room and is an almost guaranteed death if you get caught in it. Aldrich, Devourer of Gods will not usually use this attack if you've already engaged him in melee combat, but if you see Aldrich, Devourer of Gods telegraphing this attack then you need to turn and run away from him and not stop moving, because the arrows will be following behind. Dodge rolling is not enough.
Because the fight is easier if you're staying close to Aldrich, Devourer of Gods, spellcasters may find melee buff spells more effective, but Aldrich, Devourer of Gods is weak to both lightning and fire damage (high spec pyromancers in particular will be able to do a lot of damage).
Like other Lords of Cinder you've fought, Aldrich, Devourer of Gods will suddenly be on fire. His body will leave a short trail that will burn you, as if the devs knew that most players would be using a melee tactic against him. The damage from this is negligible, however, especially compared to Aldrich, Devourer of Gods' ranged attacks, so sticking up close is still preferable.
The rain of arrows attack will now go on much longer, and Aldrich, Devourer of Gods will take the opportunity to sling soul darts at you as you're running away from it, so keep moving and dodge roll forwards as soon as you hear that crystal ting sound as he casts. Aldrich, Devourer of Gods will cast some of the homing missile spells whenever he disappears now, but this is still the best opportunity to refill from your estus and ash estus flasks.
This second phase is when you're more likely to die, mainly because of that arrow attack, but if you manage to get up to him again quickly he's less likely to fire it if you've already dealt damage to him on his reappearance. The run where we killed him was one where he didn't use it at all.
We're laying it out for you here: Aldrich, Devourer of Gods may be the first boss you truly, truly hate, mainly because he'd die easily were he not a cheating son of bitch, but persevere with it. You'll get him eventually. You'll get them all eventually…
If Aldrich was your third fight with a Lord of Cinder you'll be teleported back to the High Wall of Lothric. If not you need to go back down through the Irithyll Dungeons to get to Yhorm the Giant.
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