A FEAR pokemon is a pokemon holding a focus sash/band. The pokemon also has endevour and a priority move i.e quick attack or sucker punch. FEAR pokemon are usually level 1.
The way FEAR works is that your opponent will attack this level 1 pokemon, leaving it with 1hp (thanks to the focus sash) then you use endevour which will take the enemy pokemon down to 1hp also. Use quick attack or any other priority move and that pokemon is now dead.
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The acronym only works with a few iterations of Pokémon...Treecko/Taillow are the only ones I can see that work as well (FEAT in these cases). That's not to say they're the only ones that can do this...
Heart attack, stroke, seizure, death, worse. Worse? Double death? -Wilson and House, House, MD Season 5, Under My Skin