This second Hive Queen seems to be causing a number of people problems.
When she goes to the edge of the battle area and flips upside down to fire out those bugs, zap her with the sonic attachment on the sprayer to take another notch off her life bar. She'll then fly to the other side of the arena- run to try to keep up to her and you may be able to get another hit in before she unleashes the bugs. After a few hits like this she will switch to her final attack phase.