Complex sentence: Barda has served as a member of the JLA in her own right: at Takion's order, she and fellow New God Orion are sent as agents of New Genesis to serve on the team.
Split into simpler sentences: Barda has served as a member of the JLA in her own right as well. At Takion's order, she and fellow New God Orion were sent as agents of New Genesis to serve on the team.