To get the Skeleton Key, you must have progressed reasonably far into the Power Station, have already defeated the Robotic Core, and acquired the new weapon for Rayton, the Drill.
Head back towards the terminal from where you got the Drill, and head right, defeat the enemies, and then open the Red Drill Door in front of you with the Drill. Head upwards, then use the Drills glide ability, by in midair press and hold Circle, and glide through the tunnel, avoiding the electricity on the floor.
When you have to drop down, you should hear a voice crying out for help. If you look to the bottom right of the screen, you can see a vent. Equip the Fist, and keep pressing Triangle, and this will smash the vent, allowing you to head down. Inside, you’ll find some wooden barrels, smash them all, and out of the far left barrel, you will find an NPC called Flip.
Speak to Flip, and he’ll try and charm his way out of the situation, but Rayton easily calls his bluff. Flip gives you the Skeleton Key with the promise that you never found Flip in this situation. The Skeleton Key allows you to open up any chest that is locked.
The first chest that this new key can open is in the Power Station, the one just right out the Zapper miniboss fight.
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