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i didn't discover this (all credit to community discord discussion and especially reddit user u/negmech), but i had read people discussing AI-controlled zeta, with some people saying she's amazing and some people saying she's terrible, with the dominant complaint being that she refused to perform her combo into air loops into hammer finisher.
however, there are two things you can do to mitigate this:
first, you can replace spear of arvess. for whatever reason, having this skill slotted drastically reduces the probability of her deciding to do loops.
second, and this is the preferred method and most significant impact to her damage output: you can just remove all (or most) of her skills and slot the less is more sigil. without any skills, she pretty much only does loops.
the LiM setup results in her doing among the highest damage an AI teammate can do from what i've seen, outdamaging (actual damage, not honors) or doing equivalent damage to AI eugen in many fights, particularly against single-target non-flying bosses.
on a 30s sir barrold, she can do ~13m on average with the LiM setup + glass cannon.
on a 60s sir barrold, she can do ~25m on average.
clip + gear imgur album: https://imgur.com/a/rx1pSyZ
and once again, i wouldn't have tested this if not for u/negmech's comment here: https://www.reddit.com/r/GranblueFantasyRelink/comments/1audvqz/how_to_afk_every_fight_in_proud_difficulty/kr6iq26/