Bagas is the 5th city you go to, right after you come out of the Dragon's Jaws. To be sure that the quests are active, go to the guild in Bagas and talk to the soldier at the counter - Not sure if the the quests are active until you talk to him.
Bagas QuestsDuty39 - Kaiser Draco SuppressionSuppress 10 of the Kaiser Dracos in the Dragon's Jaws -
Kaiser Dracos are the red dinosaurs that can be fought in Dragon's Jaws. There are more than enough green lizards to start a fight to kill 10 of them.Duty40 - Knight's SoulSuppress the dreadful Knight's Soul -
The Knight's Soul can be found at the beginning of the Underground Path. Go to the Chronus Shrine and through the glowing portal on the floor, once in the Underground Path go up and on the next screen immediately left onto the next area. Now take the left path up and solve the pillar puzzle. [Push the pillar on the left all the way up, turn right and push the next pillar all the way to the right. Now push the pillar below you one square down. You have to go out of the little area, so you can push the same pillar all the way to the left on the switch. With the trap gone, you can push the top pillar on top where the trap was.] You will see a soldier that you can fight by pressing 
.Duty41 - Mountain Path Monster Bird 3Suppress the Monster Bird Giberra, 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 go up and at the top you will see a path that goes to the next zone (top of the screen). When in the next area, just go up the stairs on the right until you see a big waterfall. You will then see Giberra on the right of the waterfall - bird that is not moving. Approach him and press .Duty42 - Paradise Bird SuppressionSuppress 15 of the Paradise Birds -
Paradise Birds are found on Galbure's Island. You have to take the Underground Path from the Chronus Shrine (you can only go there by advancing in the story). Once on the island walk around and you will fight the birds in random fights there.Duty43 - White Scales of WrathGather 5 White Scales of Wrath and 5 Transparent Scales -
The White Scales of Death can be found on the 4th floor in Galbure's Tower (B4F). There are two lizard enemies which will be White Dracos in fights and there is the blue sparkly thing in the midde (you have to use your ring once).Duty44 - Crimson Dragon of LegendSuppress the Crimson Dragon of Legend -
The Cromson Dragon of Legend can be found at the top floor of Elda Tower.Duty45 - Azure Dragon of LegendSuppress the Azure Dragon of Legend -
The Azure Dragon of Legend can be found at the end of the Leviathan Cave! Tip: He's vulnerable to electricity!Duty46 - Gold Dragon of LegendSuppress the gold Dragon of Legend -
The Gold Dragon can be found in the Forest of Trials. When there, take the right path and go all the way up. Next area go up again and use your ring to take the path to the right. You should see the dragon in the next area. Approach him and start the fight with .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 correct 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.