Try capturing systems with T0 or T1 planets. The alien race on the planet will have few if any turrets to defend themselves, only ship(s) with low health. Also, taking out weak one or two power empires is easier than taking out a five strength. (Caution, this starts wars.)
Buying star systems through trade routes also counts toward this.
Conquistadores were Spanish and Portuguese soldiers, explorers, and adventurers who brought much of the Americas under the control of Spain and Portugal in the 15th to 16th centuries, following Europe's discovery of the New World by Christopher Columbus in 1492.