Red Bird is a unique monster, which does not give any XP for defeating it; instead the heroes will be awarded with 1000 gold and a Phoenix Plume. It is found around Furni and Evergreen Forest.
The Red Bird is immune to any physical attacks directed at it, but will take 1 HP of damage from any magic attack. Red bird has a high Magic Evade, and will run away. Using Dragoon Magic is an easy way of taking care of one, especially if the party includes Meru, who can have more turns than others due to her speed.
The Red Bird's melee attacks will do 10% HP damage (5% while defending) regardless of the character's defense.
While Dragoon magic is effective, consider buying a couple Spark Net items in Dennigrad. They cost 10 gold and can be useful if you don't like to wait for the Dragoon Magic Animations. It's cost-effective since you'll gain 1,000 gold and on average lose 60-120 gold per kill of the Red Bird. It also saves you MP and wasting time getting your SP levels as well as resting at an Inn. The Tiara's (female helm only) and Wargod Amulets will increase your odds of landing magic attacks. As for all special monsters, it is recommended you find the Speed Up, Speed down, and Signet Stone repeatable items to help increase your odds of killing said monsters. Good luck.