I discovered a solution that skips 3 clicks! Here it is:

The portals will be referred to as A, B, C, and D as seen clockwise from the starting position: A and B are the two on the left, C is the raised one, and D is the lonely one off to the right.

Hint: After unlocking the switch to flip portal B, you would normally have to use the switch behind A in the white world in order to flip the recessed platform underneath the lasers, and later use two more clicks flipping the platform back around. There is a way to reach A and B without that platform.

Solution:
Use the recessed platform to go under the lasers to D, jump across to portal A (the left one) and click the switch.
Go back through A, return to the white world via C, and use the moved platform to enter B and click the switch.
Walk back through B and A and click the switch in the black world.
Go back through A and B again and click the switch.
Use the boost pad to enter A and click the switch.
Go through A and C, under the lasers to D, and click the newly revealed switch on the elevated platform.
Return through C and click the switch above you.
Here's the tricky part: Still on the elevated platform, try to jump over the laser blocking A and B. If you jump while it's coming towards you, then you should have enough time to get to the end. Should you fall down, just return via D and C. Once you succeed, enter B and click the switch.
Go back through B and A and click the switch.
Go back through A and B, back to the white world via C, and click the switch that flips portal B.
Finally, go through D, jump over to B, and finish the level!