Is it in your basement?!
Before Iron Crown can even spawn, you’ll need to find Perrin, who has made her way over to Blueberry Academy. She’s directly in front of the entrance to the Terarium, or at least right where you come out to in the southeast region of the Savanna Biome. If you talk to her, she’ll tell you that she’ll give you a “hot tip” if you can register 200 Pokemon in the Blueberry Pokedex.
Once you do so, Perrin will show you two pictures of the Paradox Pokemon, depending on your version of the game. No matter which version you have, though, the photos reveal the locations of the new Paradox Pokemon in Area Zero. The photos don’t give exact locations, but rather, a general area where these Pokemon have been seen. Iron Crown is seen overlooking at least one of the Research Stations from some sort of alcove.
The Research Station it overlooks is the very first one, so it is very very early in Area Zero. Go to the Zero Gate and don’t fast travel to any of the Research Stations; simply walk out of the hangar door and come to the original entrance of Area Zero.
Not far from where you begin, there is a series of slopes that head up and make it to an alcove that has a gigantic pillar in the middle of it. You wind up being very close to being directly above the entrance. From here, gauge the vantage point and see if it matches with where Iron Crown was.
If you’re in the right place, Iron Crown will be on the other side of the giant pillar, where you can approach it and battle to catch it. It is a Steel/Psychic type that knows an array of moves for type coverage: Sacred Sword, Future Sight, Volt Switch, and its exclusive never-misses move Tachyon Cutter.
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Hope this helps!