Seeing how only 2% of players had this easy and simple achievement (as of publishing this guide) and hat, I’ve made a step by step walkthrough on getting them.
Step 1: Turn on Beast Mode in the Options
Pause the game and go toOptions > Game
(The wrench icon followed by the bullet kin icon)
Turn “Beastmode” on.
Note: If we talk to the left guard at the entrance after we attempt to exit the Gungeon, he’ll ask us if we beat the game. Responding “Yes” will lead him/her/it telling you that you are ready for beastmode.

Step 2: Win
Once you’ve turned Beastmode on, Exit the Gungeon and defeat the level five boss, The Last Dragun.
Once you beat the game, you should get the achievement “Win”.
Step 3: Turn Beastmode to Level 2
Return to the settings and change Beastmode from “ON” to “LVL 2”.Note: If we talk to the left guard after beating the game with Beastmode on, we’ll get similar dialogue but we’ll be told about Beastmode level two.

Step 4: Win Again
Once you’ve turned Beastmode to “LVL 2”, you have to beat the game again.
Step 6: Talk to Left Entrance Guard Again
Once you beat the game with Beastmode Level 2, return to the Under-Breach and talk to the left guard again. The guard will congratulate you and the character you are playing as will equip the hat “The Beast”.
IMPORTANT SIDENOTE[/b]
If you don’t haven’t yet unlocked Hattori, you will not be able to unequip the hat until for the character equipped with it until you do so.
By HoD zNochan