Okay, this is a bit difficult. We need to daisy chain the sirens up.
The first step is to just redirect the beam, so grab the one redirection cube on the floor and put a portal above the spot where the laser hits. Go up and redirect it into the first siren.
The next step is where it gets tricky. The only way to fling yourself around is to put one portal above the spring and drop down onto it, with another one nearby to throw you straight up into the air. Start in front of the portal, and start the cycle of hitting the spring and being throw into the air. You can then shoot another portal onto one of the various white walls to be flung to the spot you need to go. Remember to keep track of your portals. You need to swap it out so that instead of falling onto the spring again, you “fall" into the original portal and out of a launch spot.
Start by grabbing the next redirection cube. To carry a cube, you’ll need to begin the spring process again while carrying the cube. You can let go of it at the height of your jump, so that you can shoot a new portal, and still grab it before you go through the portal. It should fall at the same speed as you. Just let go, don’t toss it.
Use this to sling shot over to the one lit siren, and direct the beam over to the second siren by the starting point.
The third redirection cube is on a high and very small platform across from the exit. You need to slingshot yourself into it, using the same trick. You should be able to do it if you aim at the highest point on the wall next to it.
If all goes well, you’ll knock the cube down onto the starting area, and land there yourself. Use the beam to blow up the turrets guarding the exit, and then power up the receiver. This forms the platform we need to escape.
Repeat the slingshot trick one more time to slingshot to the exit and the elevator.