This boss can be tough without the right android.
I used Starch and suddenly Vespula was very easy and I defeated her on my first try with Starch.
The trick here is to keep you distance. Starch's laser allows her to fire at Vespula even from the opposite side of the arena. Vespula has three types of attack. Between each wave she will drop a battery and a power up. Get the battery as soon as you can, but it's worth waiting for the increased fire power before you collect the power up.
Firstly she will surround herself with hundreds of small flying drones. Keep your laser focused on them from a mid distance while occasionally using your power attack
Next she will fire a combination of the blue bullet bombs, and then large red discs which can be a problem if you're too close. Getting as much range between you and the boss is key here, making her attacks useless against you. Keep you laser trained on Vespula constantly, try to make permanent contact with your main weapon.
You get one rotation of these attacks before you get another stage of drones followed by Vespula spawning thorny vines on the map mixed with waves of blue bullets. Again keep you distance, and keep you laser focused on the enemy whilst avoiding attacks. If you find yourself getting close, use your power attack to deal extra damage.
One more drone wave is folled by more vines and bullet bombs and masses of red discs. Keep your cool here and focus your laser on Vespula from a distance, using power attacks when she gets close and you should finish her off easily enough.