I will outline the basic strategies I used to defeat the final boss on PS4 and Vita. I hope they help you too.
The final boss is on Stage 8-2. It is incredibly annoying compared to the rest of the game.
The boss 'room' is broken into three platforms. Each gap in the room will occasionally throw a fireball up into the air. It's important to note these are the weakest thing in the room. They hit for 1HP and can be used to save yourself from one of the bosses attacks if you're unable to reach safety in time.
The boss itself has three attacks. A dash attack, a patterned shooting attack, and then a rocket attack where several rockets just randomly fall.
You should be on the center platform the vast majority of the fight. This is because you do not want to get caught by the charge attack. Centering yourself allowed you to reach the left and right platforms in time to avoid it. It also allows you more space to avoid the patterned shooting attack.
You will rely on two weapons the entire fight. The electric shot and the flamethrower. Use the electric shot the entire fight by bouncing it off the middle of the walls of the room. This ensures it splits off straight ahead and can hit the boss in the head and body. It also will cover the path it flies across while shooting the 'bullets.' The only time you want to use the flamethrower is during a rocket attack. The boss moves over one of the two gaps. Switch to the flamethrower and light it up. It is a stronger weapon than the electric weapon and it rapidly hits the stationary boss. YOUR BOSS FIGHT WILL BE MUCH FASTER DOING THIS. Also remember though, the rockets are randomized. You might not get hit during this phase, you might get hit three times, but using the flamethrower deals a lot of damage.
For the charge attack, the boss will move to one of the bottom corners. Immediately run to the opposite corner while aiming your electric shot straight ahead. The shots will bounce straight back for several hits when it charges you. Pay attention to the fireballs and just jump the gaps. If the boss is charging and you think the fireball will come up and hit you, just jump the gap and take the 1HP (or your timing was off and you don't get hit) over the bosses 4HP hit. Just remember to reset to the center platform immediately. The boss can link up multiple attacks and it can, and will, switch sides.
To avoid the patterned projectile attack, stand in the center platform. The boss will fire its first shot and it's unlike the others. It doesn't have as much of a slope to it. Quickly run under it and run towards whichever gap the boss flies over. You will have to wait for a second attack that comes towards the ground, but then you should be behind the boss and it should be easy to dodge the remaining projectiles. Just keep shooting that electric shot off the center of the walls.
With a lot of luck, you should be able to defeat the boss in half the time it would take using just the electric shot. Hopefully without too many deaths to boot.
If anyone needs screenshots for the explanations, please ask and I will do my best to quickly provide them. I tried to explain them as best as I could.