Petitioner for this hunt is bard called Fermon. He can be found in Old Archades surrounded by group of kids.
He'll tell you about a mythic monster, which is said to posses the power do destroy whole world and which has recently awaken. He asks you to deal with him.
You can find the dragon in Tchita Uplands, but it only appears when it's cloudy. Here unfortunately the weather doesn't change from sunny to rainy just while passing from one area to the other. You have to leave the whole area (e.g. to Cerobi Steppe) and get back to make the weather to change. Only remember that rainy and cloudy is almost the same, because this weather change you can observe simply changing the areas.
About 210 000 HP
Resistant to Libra,
Vulnerable to Wind
Lindwyrm's attacks are:
Besides at the end of the battle his defense raises dramatically.
Attack him using Aeroga or using a weapon with Wind element. When you dispose about half of his HP he'll use Greater Barrier - immediately cast Dispel when he does that and finish the fight.
Bounty: 4200 gil, Barrel Coat, Hi-Ether