Plant Sphere is a sphere-like ghost that lives in plant-like structures created by Insect Trapper. When approached, it will shoot three bolts of electricity at once, but if you're careful you will find a sweet spot between the two lower bolts. You can crouch in this location without moving and not get hit by any bolts.
When a Plant Sphere is blocking your path you can kill it - they respawn the minute they're no longer in view - OR you can bum-rush past it without killing it. This option is not recommended, but in some cases it's the easiest. To accomplish this you will wind up going splat several times, you'll take damage, AND you'll have to figure out a workable combination of shoot, jump, duck, and sprint.
To kill a Plant Sphere: Bombs don't work on these guys, and I've had no good results with explosives either. You have two options: regular shot or triple shot. If you choose regular shot, you'll need to get into a rhythm of shoot several times, crouch in the safe zone to evade the bolts, then hop up and repeat until the sphere is gone. This can be risky because your character may move between ducks and wind up zapped. If you use the triple shot weapon - found in the weapon store and proclaimed 'not that great' - you can simply lie on you belly in the safe zone and hammer the Sphere Ghost with triple shot. Every blast will result in two of three hits, the ghost will die quickly and painlessly, and you don't have to worry about ducking and getting shot anyway. Win-win.