This 2nd Boss has a pattern just like the first.
The man in the Tube will come down, firing lazers to the side. You can take a couple pock shots at him before hand and drop a bomb below where he'll be before jumping to the 2nd story as he fires.
He will then move upward, and fire again. This time, run underneath him.
He'll begin to charge his electricity, if you look at the probes, only 1 will not be red, stand there and he will light up the room except that spot.
Now he will fire a ball of energy downward while also blocking the top platforms. Once the ball hits the floor it will split in two and begin travelling along the ground, before bouncing off the wall back to the center, and will do this about 4 or 5 times. Plant a bomb below/next to him as he comes down, jumping over the balls of energy, and keep firing at him. (You don't need weapon upgrades at all, but they help make it go quicker)
He will then cycle back eventually to the first wave of firing the lazers sideways, and will repeat this pattern. Keep at it and he'll drop.