Gaal calculates the Raven's destination from nothing other than publicly available star charts and the few data-points the ship is not programmed to withhold from her.
Season 2
It takes Vault-AI Seldon less than thirty seconds to figure out the fact that he is not the only copy of the original human Seldon, the plan for a Second Foundation, and his position vis-a-vis his counterpart, all on the basis of two sentences' worth of relatively sparse information from Salvor.
The extent to which Dusk, Rue, Sareth and Dawn manage to discover and frustrate Demerzel's control of the Empire over the course of the last three episodes, while under constant surveillance from the system she controls.
As revealed in "Creation Myths", Gaal managed to save Hari's life using only her telepathic powers, get him to a safe place far away, continuously maintain an illusion that a substitute corpse was in fact Hari for at least a day, and keep all of it out of her conscious thoughts the whole time in order to fool Tellem.
General Riose's No-Holds-Barred Beatdown of Cleon XVII, intentional loss in the fight, and use of the castling device to get the Emperor to throw himself out of an airlock, ridding the galaxy of his particular twist on Cleonic cruelty and megalomania.
