It was several years ago, I don't have a 126 any longer, but as I recall the battery side was easier. If I had to remove the battery, that isn't such a big deal. On the fuse box side I believe I detached it, but didn't remove it completely. This gave access to the the U-clamp underneath. I do remember that it took some time and was a pain. BUT, not as bad a job as some had told me.
After getting both U-clamps off, I pulled on the sway-bar by reaching inside the fender to get enough clearance under the bar to get the old bushing out. There is a plastic dust shield, I believe, that covers where the sway-bar goes from the inner fender area into the engine compartment.
The bushings just don't flop out. They are well seated and I had to use maybe a long handled screw driver to "convince" it to pop out.
BTW, I jacked the car up, but only a little bit by the center cross-bar. Jacking one side only will create a twisting which would be hard to fight in trying to get the rubber bushing out.
Let me know if this helps.
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'65 911 Coupe (#302580)