1 Amygdala's Chamber
To get to Amygdala's Chamber, you must find the Nightmare Frontier first, which can be accessed by unlocking a door in Lecture Building.
2 Skip the laser beam
As soon as you enter Amygdala's Chamber, run and roll forwards to avoid the laser beam from hitting you.
3 Stay under Amygdala's
Amygdala has many arms and a reach that makes it nearly impossible to get in range unless you go under Amygdala's body.
4 Use fire, bolt or arcane
Amygdala is weak to fire, bolt and arcane. The recommended weapons to use are Ludwig's Holy Blade in its two handed form with Bolt or Arcane applied because it can cause massive amounts of damage with each hit or the Tonitrus charged. (See How to defeat Cleric Beast – Bloodborne?)
5 Aim for the arms
Amygdala takes massive amounts of damage to the hands or the head. However, the arms are more accessible if you do not lock-on target. The legs are weak, too, but they take less damage and the tail takes little damage, too.
6 Roll the jumping attack
After a few hits, Amygdala will jump up and attempt to land on you. This is easy to skip if you roll once and lock back on target to get there fast. (See Why Playstation 4 is good?)
7 Recommended minimum requirements
Level: 55+ Weapon: Ludwig's Holy Blade (Two handed) 2 Bolt paper/2 fire paper/Empty Phantasm Shell 8+ Blood Vials 8+ Quicksilver Bullets.