Iatt is the 4th city you go to, right after you come out of the Iatt Path. To be sure that the quests are active, go to the guild in Iatt and talk to the soldier at the counter - Not sure if the the quests are active until you talk to him.
Iatt QuestsDuty28 - Vivid Feather CollectionGather 10 Vivid Feathers -
Vivid Feathers are either accquired by defeating the Firebirds on the Iatt Path or are collected by checking out the blue sparkly things also on the Iatt Path.Duty29 - Magic Fire StonesGather 5 Magic Fire Stones and 3 Magic Fragments -
Both of the materials are best found by checking out the blue sparkly things on the Iatt path. Remember to press 
if you quickly want to leave the path to make the sparkles re-appear again.Duty30 - Magic Ice StonesGather 5 Magic Ice Stones and 3 Magic Fragments -
Both of the materials are best found by checking out the blue sparkly things on the Iatt path. Remember to press if you quickly want to leave the path to make the sparkles re-appear again.Duty31 - Magic Thunder StonesGather 5 Magic Thunder Stones and 3 Magic Fragments -
Both of the materials are best found by checking out the blue sparkly things on the Iatt path. Remember to press if you quickly want to leave the path to make the sparkles re-appear again.Duty32 - Mountain Path Monster BirdSuppress the Monster Bird Gilmoth, whose base is the Iatt Path -
Enter the Iatt Path from the west side - press when on the world map and select Iatt Path (West). Follow the path an onto the next screen, when there stay at the bottom and go right follow the path going up until you can see a "hairpin" turn going down again. You will see the bird boss on the muddy ground, a chest and blue sparkles. Approach him and press 
.Duty33 - Firebird SuppressionSuppress 10 of the Firebirds along the Iatt Path -
Like the description already tells you these Firebirds are found on the Iatt Path - defeat 10 to turn in this quest.Duty34 - Devil Papancho SuppressionSuppress the Devil Papanchos in the Forest of Trials -
For this quest you have to kill 10 Red Devil Papanchos and also 10 Blue Devil Papanchos. There are plenty in the Forest of Trials south of Iatt.Duty35 - Deluxe Fur CollectionGather 5 pieces of Deluxe Fur -
Deluxe Fur is either accquired by defeating the wolfs in the Forest of Trials (rare) or are collected by checking out the blue sparkly things also on the Forest of Trials.Duty36 - Red Devil in the ForestSuppress the Red Devil Papancho Boss in the Forest of Trials -
Go to the Forest of Trials south of Iatt. Once there, take the right path. On the next go up, staying more on the left side and as soon as you see the first path that goes left to the another area, go left. You will come into a small area with 2 moving Panchos, one chest and one Pancho that doesn't move. Approach him and start a fight with .Duty37 - Blue Devil in the ForestSuppress the Blue Devil Papancho Boss in the Forest of Trials -
Go to the Forest of Trials south of Iatt. Once there, take the left path using your ring. Go up to the next screen. On the next screen go up, but stay on the righ side of the screen. As soon as you're in the next area, turn left and you will see a rock blocking a small path through trees. Destroy the rock with 
and follow the path. You will be in a small area with 2 chests, 1 blue sparkle and one Pancho that doesn't move. Approach him and start a fight with .Duty38 - Mountain Path Monster Bird 2Suppress the Monster Bird Golteth, whose base is the Iatt Path -
You will get this quest as soon as your ring was made better by the guy (Cordea) in the tavern in Iatt. Enter the Iatt Path from the west side - press when on the world map and select Iatt Path (West). Follow the path an onto the next screen, when there go a little bit up and right twice until you can go right to the next area. On this screen go all right until you have to use your ring again, use it to cross the gap and follow the path. You will see a moving bird, a chest and the boss bird (not moving). Approach him and press .When you have completed one of the above quest, you will see a bag of money with the $ sign next to the respective duty. As soon as you collect the quest reward, the bag of will change from the $ to a star sign (blue star sign means a one-time only quest). That means that you completed the quest. You can also press
go to "Quests" and select "Quests" from the menu. You will then see the exact same stats as the soldier at the guild counter will show you.
Notes:
- Re-entering rooms or "dungeons" will respawn not only the enemies but also the blue sparkly things (the blue sparkly things will only respawn if you leave to the world map!), giving you the possibility to farm the required materials for quests.
- When you completed a quest, you will still be able to complete it again for as many times you like. You just have to go to the right city guild which gave you the completed quest(s). But remember that if you collect certain materials, the amount that you had to collect for the quest will be taken away from your inventory.