Sidequests - ToS:DoNW
There are many side quests within Tales of Symphonia: Dawn of the New World and many of them branch off into multiple chapters requiring you to go to a certain location to continue so please note the chapters of the parts of the sidequests.
This sidequest spans many chapters so make sure you pay attention to when you have to go to different locations
Part 1: Chapter 2: Simply speak to Koton in his house at Hakonesia Peak.
Part 2: Chapter 4: After going into Izoold back track and enter Hakonesia Peak. You'll see Richter enter Koton's house and are given the option to go see him or not. Choose to go see him and you will leave Marta and the others behind and go into Koton's house. Richter and Emil talk for a bit then you are told to go to Asgard. Richter sets up something to get Marta and the others away from you and then meet him at the 2nd floor of the inn. Next you have to find Linar who is located in Aishas House. Then head over to to the stone dias and re-enter the Asgard Ruins. Near the bells you'll see a harpy statue. Examine it to find a button that will open a door leading to a portal to the Balacruf Mausoleum. Change the sorcerer's ring to the wind element in the room near the entrance and continue through the Mausoleum. When you get to the room with the windmills you can put in different combinations to get items but to continue on the quest hit them in the following order: Red, Yellow, Green, White, Blue. You can go up ahead to face a phoenix if you are about level 50 or higher to get some good items but otherwise go down. The floor below is a maze of pushing and pulling blocks. Navigate your way through and you'll come across some treasure chests and the Balacruf Tombstone which is protected by some monsters. After beating the monsters, leave the ruins and this part of the quest is done.
Part 3: Chapter 4: After you recieve the Jellyfish, leave and re-enter Triet. You will notice a long line leading to the fortune tellers tent and find out she is giving free fortunes. You soon find out that Richter is in town and have the option to go see him while Marta wait in line for a fortune. Now you have to take Richter to Camberto Caves where you found the rosemary so he can get a bug called the Angelatops. Afterword you'll be taken to Iselia, where you need to go to Collete's house (North East of the entrance). There is some dialogue and then this part of the quest is completed
Part 4: Chapter 6: As long as you did the rest of the parts of this side quest this one will start automatically upon entering the Academy Institute. Richter will offer you to follow him to Cape Fortress. So head off to Cape Fortress where you'll meet up with Richter alone. Navigate through the Fortress and when you get to the statues, change the sorcerer's ring to the water element and put out the fires in the following order: lower left, middle left, middle right, upper right, lower right, upper left. Press the button at the foot of the blue knight and the path will open. Continue on the path until you find a book and then you are taken to Meltokio and you have finished the Richter sidequest.
Twlight Palace Sidequest
Part 1: Chapter 5: Complete the "Treasure Hunter's Trophy" quest offered by the Katz.
Part 2: Chapter 6: Complete the "Treasure Hunter's Trophy" quest offered by the Katz.
Part 3: Chapter 7: Complete the "Treasure Hunter's Trophy" quest offered by the Katz.
Part 4: Chapter 8: Complete the "Treasure Hunter's Trophy" quest offered by the Katz. This one is a little different though. The other quests will take place on one of the generic maps but this one is a brand new map with many rare weapons and armor hidden in chests, many of these items being the best Emil or Marta can get. So make sure you search for all of the chests and get the items as they will help you later in the quest. You will have to face 3 mini-bosses and then the feared Album Atrum as the final Boss. Album's face changes to one of three faces, one has physical resistance, one has magical resisitance and one has no resistances. Plan your attacks carefully according to his face. Also it is a good idea to have skills that increase item drop rate as Album has a 5% chance to drop Kismet, Marta's final and strongest weapon in the game. When you complete the quest you will be given Emil's best weapon, the Nether Traitor, and a rare monster called a Kitty Kat.
This optional dungeon is only available in the second playthrough. Gladsheim is the most difficult dungeon in the game so make sure you are prepared to face high level monsters (though do not max out your gels as you can get many of them during your trip through the dungeon), including a level 200 Album Atrum on the final floor. Also, something to know is this dungeon will easily take 5 hours to complete and there wont be a save point till you get to the 3rd floor so make sure you have the time to get that far. To advance to the next floor you must reach the corners of the 8x8 square and fight the non-archdemon monster atop it. Save points are available on floors 3 and 6 though they are yellow save points and will not recover your health. On floor 10 you will be teleported into a 4 way room where each room takes you to a dead end room with Album Altrum inside. Defeat him and you will be released from Gladsheim after hours of torture.
To get a more detailed guide on navigating through Gladsheim check out Memnarch's Gamefaq Guide on Gladsheim
To get more detailed descriptions of these sidequests and more check out Kirby647's Gamefaq Sidequest Guide