The thing at the top isn't a clip so much as a guide. The top edge of the ring should fit over a lip on the headlight bucket, then the bottom edge gets pushed back until it's tab engages with the clip on the bucket.
In this shot, the lower clip is partially broken, but you can see how the tab fits into the clip. I usually had to turn the tool around backwards, and use it to push directly on the tab to get it to pop into place.
The tool is very simple, just a flat strip of metal about 1/2" wide and 4" or 5" long, with a lip turned up at one end. TRF sells a reasonable reproduction fairly cheap; or you can make your own. An old PC I/O slot cover will work, too.