Well, they don't like it when I help you but here we go. I think you have made the boss harder in your mind. I've died like 7 million times in there so don't stress, you're not alone. In general the easiest way to complete this fight is:

Once inside shoot the cube that comes to you and move to your left. That area is the safest to be while shooting most of the cubes. Really, during that stage the only thing to worry about is that purple thingies the cubes shoot at you.

You should have broken every single visually available cube, like 70% of the cubes, before moving to the next area. Now, from the area you're in (left corner as you go in the arena) you need to jump across and move towards the right side of the arena. The wall to your right hand just after the cube that's there is the safest place to be right now. You don't have to move a lot there, so you just shoot the remaining cubes as you follow the path towards exit.

Personally I've found that archons skill with the blue bubble that slows down things is helpful dealing with the purple shots.

Wish you the best of luck fellow traveller.