Coeurls in Final Fantasy Tactics Advance are powerful blue beasts that are related to Red Panthers. They have a large amount of HP and are very dangerous to approach because of their "Blaster" skill and high Attack power. Luckily, there is usually never any more than 1 Coeurl at a time.
It's a good idea for your units to use the Judge and easternmost cactus to cover their backs when heading for the Couerl.
Complete Mission #003: The Cheetahs
Mission #004: Desert Peril
The Couerl here starts off on a mesa and should take at least 3 turns to reach the party. Try to eliminate the closer enemies before the blue panther catches up with you.
The 4 escaped monsters here should be no match for your party, unless the Ahrimans begins to KO most of your units with Roulette and the Couerl petrifies the rest with "Blaster".
Complete Mission #012: Pale Company
Mission #052: Friend Trouble
There are 3 Red Panthers and a Couerl here. Try not to let them surround your mages.
Complete Mission #016: The Big Find
Mission #065: Exploration
To unlock Jagd Ahli, you'll need to defeat the monsters guarding the gate. The Couerl starts off on the left side of the screen.
Complete Mission #021: Hidden Vein
Mission #022: To Ambervale
The Couerl here is backed up a a group of other difficult monsters, including a Big Malboro, Thundrake, and Lilith.
Complete Mission #191: Lucky Charm
Mission #067: Missing Meow
The runaway level 35 Couerl here does everything but meow. Disabling it or putting it to sleep helps a lot.