The series's defining moment of triumph, the ending of 'The Last Colony'. John Perry finally gets his revenge on the Colonial Union, fatally destabilising it and freeing humanity from its grasp with a well-placed trading convoy.
The five Consu duels to confirm the help they gave the Rraey. Ending with Jane the Combat Pragmatist taking advantage of the Screaming Warrior nature of the Consu she's fighting - while he's bellowing a war cry, she throws her knife through the roof of his mouth and into his primary braincase.
An earlier moment in The Last Colony, in which General Gau is (unknowingly) about to be utterly outmaneuvered by the CDF. John Perry jeopardizes the success of the maneuver (which relies on total surprise) by offering Gau a chance to surrender - out of compassion for the unsuspecting crews of Gau's space armada.