I have a toilet seat that is loose, but can not work out how to tighten it. I looked under the fitting but there is no nut. It looks like the end of the bolt is designed not to turn.
All the work needs to be done on the top.
See that metal disk on the left in the picture of the top-side. Press it in and its partner, and remove the seat/lid (by lifting off).
Now remove the large (one inch-ish) covers that remain. Now you can see the top of the screw. Tighten screws.
Put everything back.
To align the pins, turn seat upside down, and try to align. This worked good enough for me. I had no trouble with alignment.