Star Ocean: The Last Hope - Complete Post-Purgatorium Quests

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Several new quests are available now. Completing them may lead to other quests or open up new things. After leaving the Purgatorium, stop at Tropp. You can open the last two Treasure Chests in town now that you have the Light Ring. Since it only holds one charge, you will have to go back to a Light Crystal in the Purgatorium after opening a chest to charge the ring before you can open the other. Then talk to the people of Tropp to accept new quests.

New Quests - Tropp

The Ex-Cultist near the town entrance used to be a merchant and wants to go straight now, but he donated all his money to the Church of Sydonai. He needs some new clothes and will give you the New Life, New Clothes quest.
If you gave some Otherworldly Cuisine to the Overweight Woman and at least 2 hours have passed in the game since you completed her quest, she will offer you the Rebound Queen quest.
The lady from the Doll quests inside the Inn will ask for your help with the Whodunit? quest.
The Retired Explorer west of town square asks you to undertake his Desert Dilemma quest.
Complete the Ex-Cultist's New Life, New Clothes quest and he will reveal himself to be Ruddle. He wants to go to Tatroi and will have The Mapless Traveler quest for you. If you have a Map of Astral in your inventory, you can complete the quest right away.
Leave Tropp and return. You will find Ruddle at the docks and he will have the Ruddle Strikes Again quest.
After you complete the Desert Dilemma quest, the Retired Explorer wants you to take on his The Sand Bird Strikes Back quest.

If you complete both the Desert Dilemma and The Sand Bird Strikes Back quests, the quicksand trenches in the Astral Desert and Tropp Area will become normal sand. You won't need a bunny to cross the desert any more. You will have to talk to the Retired Explorer at the oasis and again at the Tatroi inn to receive a reward for the second quest.

Cactus Rescue

The best time to do The Desert Cacti side quest is after you complete the Sand Bird quests. It is much easier to navigate the desert once the quicksand is gone.

Meracle's Ocarina

Part of your reward for completing the second Sand Bird quest is the Skill Manual "Ocarina". Teach the skill to Meracle and she can use it from the Skills menu to recall nearby enemies that you recently defeated. It is a very useful skill if you are trying to raise the analysis level of a particular monster or want to keep fighting the same type of monster to obtain a specific item drop.

After you complete the quests above (or while you are working on them) you can take on some more new quests in Tatroi.

New Quests - Tatroi and Astral City

If you completed the Ruddle quests and the Sand Bird quests in Tropp, you will find Ruddle peddling his wares on the opposite side of the street from Black Cat Materials. Stop by to look over his stock and to accept his Shop Orders.

Completing the Sand Bird quests also allowed Chaz to return to Tatroi, and he has set up his own Skill Manual Shop at Twin Books.

Head north, past the statue and have the Suspicious Psychokineticist charge your Disintegration Rings, especially the Light Ring. Then you can start talking to townsfolk and accept some new quests.

Talk to the Diligent Clerk near the entrance to the Colosseum and she will ask you to take on her Where's the Receptionist? quest.
You'll need to go to Astral City to complete the Where's the Receptionist quest. When you find the missing Receptionist, she wants you to fulfill her Sore Throat Soother quest before she will go back to Tatroi.
While you are in Astral City, talk to the Woozy Man near the canal barge to receive the No Way Home quest.
Before leaving Astral City, use the Light Ring to open the sealed chest inside the residence southwest of the canal barge.
After you complete the Sore Throat Soother quest, the receptionist will go back to work and they will open the Colosseum in Tatroi. Go inside to check things out. You will need to talk to the Diligent Clerk in the lobby area inside the Colosseum to get your reward for the Where's the Receptionist? quest. Then talk to Lucy, the Receptionist, and the Colosseum's battle tournaments will become available.
Downstairs at the Colosseum, you can talk to the Chatty Bunny Trainer and get the Listless Bunny quest.
Speak with the Mischievous Woman in the northeast mansion. She wants you to accept the Puffy's Debut quest.
Return to the mansion after completing the Puffy's Debut quest to get your reward. Leave the mansion and return to receive the Puffy's Rage quest.
Puffy's not satisfied yet. Go back to the mansion again and accept her Puffy's Revenge quest.

Before leaving Tatroi, have the Suspicious Psychokineticist charge your Light Ring again.

Leaving Roak

Once you have had your fill of questing, head back to the Calnus. A scene will occur as you enter the ship and Welch will have new orders for you and your team.