As The Paradox, defeat the Lich. This will launch you into a new run as the Gunslinger at the beginning of the first chamber. It is important to note that at this stage, you have not unlocked him, you’ve merely unlocked a single attempt at unlocking him permanently. If you die, quick restart, or exit the game without using save button before finishing his run, you will have to start the process over by beginning another run as The Paradox. To unlock him permanently, you must proceed through the game again, making sure to get The Bullet That Can Kill The Past from the blacksmith in The Forge (if you don’t get the Bullet before entering the Nameless Void, then firing The Gun That Can Kill The Past will simply send the game straight to the credits, and you will have to begin the process again with another Paradox run) and kill his past (See: Past Kill).