Tightening a bathroom faucet
I have no experience with this type of faucet, but from the picture it appears it is held in place only in the center. There are several possible ways the hinged clamp in the center may work. Is the hinged clamp in fact holding the body of the faucet or is this just a connection to the drain plug?

It may be that you pull down on the rod and press up on the clamp. It may be that you have to pinch the side tabs together to move the clamp up or it may be that the tabs are to be pressed only to remove the clamp.

It may be that you twist the clamp with or without pinching the tabs together.