The Perplex is the main story mode of Horizon Zero, and takes many elements from the Classic and Adventure modes from Super Smash Bros. Melee. It focuses on Sheddane and her goal to stop the evil Black Doom from taking over the Horizon Zero landscape.
The Perplex opens up with a cinematic introduction, which can be skipped, leading the player to the first level, which is always Hynau. Once you pass through this stage, you'll go through any of the other stages in random order, and you'll go through a total of 8/10/12/16/20, depending on your chosen difficulty. Every two stages, you fight a boss, and after the last stage, you'll fight Black Doom or someone in higher rank. The third to last stage has you fighting Metal Athena in Normal or higher difficulties.
Each stage is a short level with its own unique gimmicks that you must cross. For example, the Ghost Zone stage has you going through a maze of floating doors and low gravity. Sometimes, as you go through these stages, you'll fight other characters, whom you can recruit for your team. After you make it to the end of each provided level, your score will be tallied and you'll move to the next stage, or a boss if you have completed an even-numbered stage.
Bosses have higher health than usual fighters and sport special movesets as their own. You cannot recruit bosses, you can only defeat them, and once you defeat them, they won't appear for the rest of your round of the Perplex. Defeating a boss requires strategy and a few good skills, and if you don't know how to fight in this game, you might as well be defeated easily and crushed to a bloody pulp. Examples of strong bosses in this game include Black Doom and the Father.
When you fight opponents, you can choose to kill them or recruit them. If you kill them, you'll get point bonuses and some of their weapons, but you have limited lives to use against Black Doom. When you recruit opponents, you don't get point bonuses or items, but you'll have more chances against Black Doom.
Sheddane was a powerful demon back in her day, but she collapsed and died back in the late 1100s thanks to hypothermia where she lived. Recently though, she was resurrected in the depths of Hell, and looked rather beat up and torn apart. The people who brought her back smiled and held her up, and explained why she was resurrected. Recently, Black Doom was revived following his defeat in Shadow the Hedgehog, and is now taking over the Horizon Zero landscape, with the Black Arms everywhere. Sheddane boiled in anger at the thought of Black Doom, and stormed out of the laboratory, dropping a bomb to destroy it, killing the people who brought her back.
From this point forward, Sheddane will go through a randomized set of stages, the amount in that set being dependent on the game's difficulty level setting. Once she makes it to the final level, she will come across Black Doom and fight him, alongside any allies that she has brought along with her on her journey.
After defeating Black Doom, Sheddane wickedly smiled and slashed through his behind, tearing through to his heart and effectively killing him. She then walked away, dragging his corpse with her, coming across a phoenix-like lady. She grinned and pawed at the ground, meowing to get her attention, and depending on how much has been killed or recruited, she'll kill you at the spot or take you to her home, respectively.