Defeat hive queen is the name given to two different missions in Daxter. Each mission involves a boss fight against a different kind of hive queen.
The first mission occurs at the end of the "Take care of bugs in transit system" mission. After a train chase deep down in the transit system, Daxter accidentally ran into the Altum sonatur queen and subsequently defeated it.
The second mission is a follow up to the Miner's plan involving smashing the hives at the strip mine. The crushed hives ended up luring the hive queen into a trap, at which point Daxter proceeded to fight and eventually kill it.