I didn't use Geos to unlock her, so I can't be certain.
I hear good things about Brood Alpha making the event easy, and the superstar of your squad is going to be GeoSpy who can one-shot Padmé or her allies if they have just a few buffs (and Padmé's squad acquires a lot of buffs). So I would definitely give it a try.
Mod Spy for Damage - don't worry about speed. You gain TM when other Geos land debuffs, and Soldier is going to passing out a lot of TenacityDOWN. Zeta Brood Alpha's summon if you can.
The order in which you place the Geos in your squad is going to matter, since it calls the ally assists in order that the characters were placed in the squad. Obviously Brood Alpha has to be #1 because that's the leadership slot.
After that, however, Sun Fac should be in slot #2 (because he dispells buffs), then Soldier (to inflict TenacityDOWN) and only then do you want Poggle (for Ability Block). Spy is your last toon.
Note that this has no effect on speed. It only matters for the order in which assists are called.
Go ahead and let buffs stack up on characters you want to one-shot with spy. Don't use other Geos to attack them to "soften them up" because then Sun Fac would inflict a dispel, and what's really going to kill them is Spy's bonus damage from their buffs.
There are videos that will go into more detail, I'm sure. Good luck.