
You can pace back and forth along a wall, or up and down the stairs to the bottom floor while spamming his head with Fire Spray. As soon as you emerge from the fog, run to the stairs on the right.If you accidentally fall to the ground level, try to quickly get back to the middle level.
You will have to negotiate the stairs during your run. The role of the half-circuit is to get you out of his attack arc when you stop to cast the spell. There is no need to even look at him so you can concentrate on running. With a powerful caster, two casts are enough to kill the demon even in New Game++. The spell will automatically hit the demon and it will quickly kill him. After every half-circuit, cast Homing Soul Arrow again. After completing a half-circuit or so, cast Homing Soul Arrow.
Start running around the level counterclockwise. Middle Level Strategy - Homing Soul Arrow This way you can kill him without ever getting hit. You can then walk out to the edge, shoot his head, and back-up to the doorway (rolling back also helps).
Note: If you keep your back against the fog-doorway, you will be out of range of his tongue lash. If you are lucky, his tongue will never hit you. It is best to look down and shoot him till he is almost below you, then quickly run to the other side and repeat. The Adjudicator's weak spot from up here is his head, specifically the brown bird nesting in his crown. If you insist on fighting from the upper tiers then it is best to hug the wall with the Thief's Ring on and don't stay still. You can fire at the Adjudicator from any of the tiers, but he will lash out his tongue at you and break away sections of the floor.