The final boss is the 'Sisters' who you will face at the end of the 'Eternity' world. The boss is actually pretty easy when you learn the pattern. There are three stages:
Stage 1: As you come up onto the screen, you will see coloured beams coming from the sisters in the central ball and a spray of coloured bullet will begin. You have to hit the end of all the beams. There are approx five to hit in this stage. The easiest way to do this, and get yourself used to the polarity changes, is to stand on the middle right outer platform. If you stand right at the end of the platform, the side closest to the sisters, you will not get hit because the coloured waves sweep over and below you. Just stand on this platform and wait for the beams to cycle around to you. Smash them when they are in reach. Now hit the sisters by using your Beam attack. When their energy bar is depleted by a third, the second stage begins.
Stage 2: Now you have to deal with short and long beams and a faster wave of coloured bullets. Learn the wave pattern. It's easy but you have to change polarities every 2-3 seconds. Destroy the long beams first. The best way to do this is to stand on a platform next to a long beam and wait until you are at the very top. This is the best time to smash the end of the beams. Repeat this until all long beams are destoyed and then start working on the shorter ones in the middle. Once all are destroyed, the sisters become vulnerable again. If you have any special move left, use the Beam power. If not, time your polarity switches and hit the sisters when you can.
Stage 3: The final stage is possibly easier than the second. Blue and red rays will come out from the center, so you must be ready to switch polarities quickly. Stay on the outer platforms when you can so that you can see which colour you need to be. Like in the second stage, destroy the longer beams first, then smash the smaller ones. For the final time, choose your moments to hit the sisters. 3-4 hits and you will have done it.
There is a youtube video below, if you're still struggling with this (credit goes to HayabusaDGO for the clip)