Simple break down of the quest.

1. Get 3 inks for 500 myth each.
2. Hand in inks to get sphere scroll.
3. Infusing sphere scroll requires Alexandrite and grades 1-4 materia of the stats in question. First infusion needs to be grade 1. Total stats for each sphere scroll is 75 and the max you can get on one single stats seems to be 44 leaving you 31 left of the other stat. First infusion with a grade 1 was 100% giving you one point. This possiblly means you need 75 Alexandrite to finsh the quest unless when you can infuse grade 2-4 materia it gives more then 1 point each.

This means it might take a while and a lot of materia to finish this quest.

Getting Alexandrite -
1. Daily quest for a mysterious map gives one each day. Requires you to do the Expert Roulette(can do as a group).
2. 800 myth for more maps fro Rowena.
3. Fate grind(prob has the same drop rate as an Atma since they share the same pop-up when you get one)