Route A or Route B
Jackass's Research - 400 EXP, 4000G, 4x Medium Recovery, E-Drug
This one becomes available upon returning to the Resistance Camp after visiting the Machine Village for the first time. Jackass is at the desert section of the city ruins, near the tunnel that leads to the Desert Zone. She wants you provide her with 4 types of data by fighting enemies. Speak to her after completing a task to move on to the next one. Once you've completed all for battles, wait for a bit and you'll receive an e-mail. View it at an access point then go find Jackass at her usual spot.
Heritage of the Past - Spear of the Usurper
You can start this in Route A after obtaining the scanner pod program from Davola and Papola. In Route B, you can begin upon arriving in the Desert Zone for the first time provided you speak with the client first. For this quest, you need to find a total of 4 different relics and turn them over to the researcher. Finding all the pieces can take quite a while however due to the size of the desert. Once again, you have use the scanner to find the otherwise invisible items.
The location of the client for this cumbersome sidequest.
The location of the first relic: Ancient Stick.
The location of the second relic: Filthy Mask.
The location of the third relic: Commandment Slab (Mysterious Lithograph 2 archive).
The location of the fourth relic: Statue of a Girl. You must turn in the first three relics for this last one to appear at the spot indicated.