The first goal is to get up. There is a teleporter on the middle platform, so jump over to it. Use the switch if you don't like rockets being shot out of the teleporter. Continue onward to the next teleporter, taking care not to fall down. Out of the second teleporter, look for a floating platform moving past the small platform you are on. Step onto the floating platform and enter yet another teleporter.
Once out of the teleporter and finally in the top area of the level go to the area with colored floor areas. Only the green colored parts of the floor are solid, so jump on those areas to the other side.
Once past the fake floor, you come across Helga. Just shoot her with the helping hand like any other guard and move her under the open cage, it will drop down and capture her.
With Helga captured, and Dr. Brain freed, the path up the ramp outside will be unblocked. For the final challenge just jump onto one of the two jump pads and get up to the highest level where the exit door is.