What it stands for
 A... Not so nice version
Read at your own risk: "(bleep)ing "A"nnoying "E"vil "Rodent"
 What is F.E.A.R?
FEAR is an interesting strategy that involves a Level 1 Pokémon with the moves Quick Attack and Endeavor, holding A Focus Sash. On turn 1, use Endeavor to bring the opponent's Pokemon down to around 10 HP, give or take. Next turn involves using Quick Attack, successfully knocking out the opposing Pokemon. The Focus Sash is there in case the enemy attacks, leaving you at 1 HP.
Rattata isn't the only Pokémon capable of executing such a strategy. A variation of the strategy involves using an Aron with the Sturdy Ability whilst holding a Shell Bell. Sturdy keeps it from fainting from one attack whenever its HP is full, and after using Endeavor, the Shell Bell will fully restore Aron's HP, allowing for Sturdy to work multiple times in the same battle!
 What Counters F.E.A.R?
Fear not, as there "are" counters to said strategy, most of them are sure-fire.
Using Ghost type Pokémon: While it won't stop you from getting hit by Endeavor, it will easily block Quick Attack, and you can swiftly KO it. This counter is why some F.E.A.R Pokémon have a move that has priority, that can hit Ghost Types. The previous statement can only apply when possible.
Switching Out: As above, it won't stop you from getting Endeavor'd, but it will ruin the strategy. Forcing a substitution by phazing the FEAR Pokémon will also hinder how effective it is, but that'll happen last due to negative move priority.
Status Ailments: Status Ailments can be a massive hindrance to this strategy. While Sleep can stop the FEAR Pokémon in theory, there's also Sleep Clause to consider--if another opposing Pokémon is asleep the strategy won't work. However, while it's asleep that Pokémon can easily be disposed of with a couple of attacks.
Paralysis has a chance of its victim being unable to attack, giving a free turn to target the FEAR user.
Poison and Burn will both hinder a FEAR user that's trying to survive, and in the case of a FEAR user with Sturdy as its Ability with a Shell Bell as its Hold Item, will prevent the Ability from being activated multiple times. Steel-types can't be Poisoned, however.
Becoming Frozen is any Pokémon's worst nightmare in a tournament, however this especially holds true for a FEAR Pokémon, all but dooming it to being KO'd.
Multi-Hit Attacks: Moves that hit an opposing Pokémon are far and away the most effective way of removing a FEAR Pokémon from the field. While completely situational, it's hard to argue that anything else is more effective than a Double Kick, Water Shuriken, or any attack that hits multiple times on a FEAR Pokémon. The first hit uses the Focus Sash or triggers Sturdy, with the second hit taking it down.
Again, this is completely situational but it's highly effective. The real question is this: Is it worth sacrificing a moveslot on your Pokémon?