Once players have reached the ending in Xen when the reactor is ready, just grab the hat and hop into it together. Sometimes the hat won't pass through. Climbing backward is an easy fix for this. If necessary, let it fall from an object around the map to get it upright. At times players will also have a problem with climbing ladders. It's best to try to carry it upright and place it upright. The hat will roll away, either on its own or by getting blasted. Luckily the hat will not just disappear so if it's not immediately apparent simply look harder. Dropping the hat at opportune in a safe place to clear out rooms is required to make it through the adventure intact. While carrying the hat, players will not be able to run or shoot.
One smart tip for this achievement is to play the game on easy mode, this will make everything a lot less challenging and help with the combat sections of the game. Players must bring the hidden hat with them through the entire adventure, eventually dropping it into the reactor along with themselves at the end of the game.