You don't need to do the amity game with her to gain 1000 amity, she gives 4 quests that each gives 250 amity. However, you need to complete all storyline quests in Boulder Outpost and Shakatu before the quests unlocks.

Best I can tell Xerxes requires a quest line from Arenda in Shakatu to be complete. Arenda's questline should start once the following quests are complete and you've reached gathering: profession 10.
http://bdocodex.com/jp/quest/5709/1/

Meh was easier to get 1k amity, than getting pro 10 gathering to start her quests %D

Have anyone figured out a good order to place the knowledge in the amity game? the screenshot above was not that great for a general selection.

If that can still help people. I increased the amity with it

This is the only thing I could get to work so far.. The other combos shown in the comments give me mainly fails and I cant get any amity from them.

Good Combo

I only had three of her quests visible, the fourth one ( "Arenda's Acacia Vanity" ) did not show up for me. So my solution was to do the three quests that she had for me and spam F5 greet for the 250 missing Amity as the Amity game gave me way too many fails with 0 Amity gained.

This worked best for me:

Aidja
Muhan
Volve
Mohana
Atui Balacs
Rafa
Elfa
Amir