The battle with the Hive Queen goes in about three different stages. When you first see her she's in an egg-like shape. Hit her once and then step back and destroy the bugs she puts out. After a few hits she will come out and shoot several beams. When this is happening hop over the beams and get her with the bug spray. You can then dash behind her and swat her with the bug zapper. After a few of these she gets mad and on to phase two.
In this phase she slams the ground creating shockwaves that can easily hit you. Hover using your sprayer to avoid this and get behind her to lay i some more shots with the swatter. It won't be long before you get to the final phase. The same strategy outlined above for phase one will beat her for good here. Good luck!